Two answers in one

I've posted two answers here:

• A bash script which is hopefully easier to understand
• A one-liner using common Linux utilities grep, sed and cut

How the Bash script looks in operation

I've turned off gnome-terminal line wrap to make input and output files easier to read.

───────────────────────────────────────────────────────────────────────────────────────────
rick@alien:~/askubuntu$ tput rmam # Turn off line wrap
───────────────────────────────────────────────────────────────────────────────────────────
rick@alien:~/askubuntu$ cat aptfilein
Published repositories:
 * test_repo_one/xenial [i386,amd64] publishes {main: [xenial-main_20190311]: Snapshot from mirr}
 * test_repo_one/xenial-security [i386,amd64] publishes {main: [xenial-security-main_20190311]: }
 * test_repo_two/trusty [i386,amd64] publishes {main: [trusty-main_20190312]: Snapshot from mirr}
...
───────────────────────────────────────────────────────────────────────────────────────────
rick@alien:~/askubuntu$ time aptfileparse.sh
5 lines read from aptfilein
3 lines written to aptfileout

real    0m0.025s
user    0m0.016s
sys     0m0.004s
───────────────────────────────────────────────────────────────────────────────────────────
rick@alien:~/askubuntu$ cat aptfileout
 test_repo_one/xenial [xenial-main_20190311] [xenial-multiverse_20190311] [xenial-restricted_201]
 test_repo_one/xenial-security [xenial-security-main_20190311] [xenial-security-multiverse_20190]
 test_repo_two/trusty [trusty-main_20190312] [trusty-multiverse_20190312] [trusty-restricted_201]
───────────────────────────────────────────────────────────────────────────────────────────
rick@alien:~/askubuntu$ 

The actual Bash script

Remember to make the script executable with chmod a+x script.sh

#!/bin/bash

# NAME: aptfileparse.sh
# PATH: ~/askubuntu
# DESC: Parse Apt File giving new lines.
# DATE: July 1, 2019.
# NOTE: For: https://askubuntu.com/questions/1127821/text-processing-aptly-output-file
#       Program would be ~10 lines shorter (but harder to read) with arrays.

: <<'END'
/* -----------------------------------------------------------------------------

INPUT FILE LAYOUT
=================

Published repositories:
 * test_repo_one/xenial [i386,amd64] publishes {main: [xenial-main_20190311]: Snapshot from mirror [xenial-main]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {multiverse: [xenial-multiverse_20190311]: Snapshot from mirror [xenial-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {restricted: [xenial-restricted_20190311]: Snapshot from mirror [xenial-restricted]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {universe: [xenial-universe_20190311]: Snapshot from mirror [xenial-universe]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}
 * test_repo_one/xenial-security [i386,amd64] publishes {main: [xenial-security-main_20190311]: Snapshot from mirror [xenial-security-main]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {multiverse: [xenial-security-multiverse_20190311]: Snapshot from mirror [xenial-security-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {restricted: [xenial-security-restricted_20190311]: Snapshot from mirror [xenial-security-restricted]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {universe: [xenial-security-universe_20190311]: Snapshot from mirror [xenial-security-universe]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}
 * test_repo_two/trusty [i386,amd64] publishes {main: [trusty-main_20190312]: Snapshot from mirror [trusty-main]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {multiverse: [trusty-multiverse_20190312]: Snapshot from mirror [trusty-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {restricted: [trusty-restricted_20190312]: Snapshot from mirror [trusty-restricted]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {universe: [trusty-universe_20190312]: Snapshot from mirror [trusty-universe]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}
...

OUTPUT FILE LAYOUT
==================

 test_repo_one/xenial [xenial-main_20190311] [xenial-multiverse_20190311] [xenial-restricted_20190311] [xenial-universe_20190311]

Five fields to extract: name, main, multiverse, restricted, universe

----------------------------------------------------------------------------- */
END

 INPUT="aptfilein"
OUTPUT="aptfileout"

> "$OUTPUT" # Erase previous output file

# Read all input lines
while IFS= read -r line ; do

    let CountIn++
    ! [[ "$line" =~ " *" ]] && continue     # skip lines not starting " *"
    # Get name
    line="${line#" * "}"                    # remove leading " * "
    lout="${line%%" "*}"                    # name is up to next " "
    line="${line#" "*}"                     # remove name from line
    # Get main
    line="${line#*"{main: "}"               # remove leading "{main: "
    lout="$lout ${line%%":"*}"              # main is up to next ":"
    line="${line#":"*}"                     # remove name from line
    # Get multiverse
    line="${line#*"{multiverse: "}"         # remove leading "{multiverse: "
    lout="$lout ${line%%":"*}"              # maultiverse is up to next ":"
    line="${line#":"*}"                     # remove multiverse from line
    # Get restricted
    line="${line#*"{restricted: "}"         # remove leading "{restricted: "
    lout="$lout ${line%%":"*}"              # restricted is up to next ":"
    line="${line#":"*}"                     # remove restricted from line
    # Get universe
    line="${line#*"{universe: "}"           # remove leading "{universe: "
    lout="$lout ${line%%":"*}"              # universe is up to next ":"
    line="${line#":"*}"                     # remove universe from line

    # Append line to output file with leading space
    echo " $lout" >> "$OUTPUT"
    let CountOut++

done < "$INPUT"

echo  "$CountIn lines read from $INPUT"
echo "$CountOut lines written to $OUTPUT"

One-liner with common utilities

One-liners are popular in the Linux community and there are some excellent awk and perl answers posted in this Q&A. Here is an example using common utilities most experienced command line users are familiar with:

$ time grep ^" \*" aptfilein | sed 's/ \* //;s/ /: /;s/^/ /' | cut -d':' -f1,3,6,9,12 --output-delimiter=''
 test_repo_one/xenial [xenial-main_20190311] [xenial-multiverse_20190311] [xenial-restricted_20190311] [xenial-universe_20190311]
 test_repo_one/xenial-security [xenial-security-main_20190311] [xenial-security-multiverse_20190311] [xenial-security-restricted_20190311] [xenial-security-universe_20190311]
 test_repo_two/trusty [trusty-main_20190312] [trusty-multiverse_20190312] [trusty-restricted_20190312] [trusty-universe_20190312]

real    0m0.011s
user    0m0.003s
sys     0m0.008s

• grep ^" \*" aptfilein - the grep command selects lines containing a search string. The carrot (^) denotes the string must start at the beginning of the line. The backslash (\) denotes the asterisk/splat (*) is to be taken literally and not act as a wildcard character that selects everything. In summary this grep command selects all lines beginning with * in file aptfilein.
• sed is a "stream editor" that edits lines coming in and changes them and passes them out. There are three sed changes here 's/ \* //;s/ /: /;s/^/ /'. The changes are between quotes (') and delineated (separated) by a semi-colon (;) deliminator. They are broken down in next three points.
• s/ \* // - search first occurrence of * and change it to null. This will erase the * that begins at each line.
• s/ /: / - searches for the first space and changes it into a colon (:) followed by a space. This is necessary to change our first field into a key. For example test_repo_one/xenial becomes test_repo_one/xenial: .
• s/^/ / - tells sed to insert a space at the beginning of each line.
• cut -d':' -f1,3,6,9,12 --output-delimiter='' - Uses the cut command to select key fields # 1, 3, 6, 9 and 12. The key fields are delimited by a colon as argument -d':' stipulates. Normally output fields are delimited the same but this is overridden to null using --output-delimiter=''` parameter.

Note: The one-liner is faster than bash which is slower at string processing.

A Perl approach:

$ perl -lne 'next unless /^\s*\*\s*(\S+)/; $n=$1; @k=(/\{.+?:\s*\[(.+?)\]/g); print "$n @k"' file 
test_repo_one/xenial xenial-main_20190311 xenial-multiverse_20190311 xenial-restricted_20190311 xenial-universe_20190311
test_repo_one/xenial-security xenial-security-main_20190311 xenial-security-multiverse_20190311 xenial-security-restricted_20190311 xenial-security-universe_20190311
test_repo_two/trusty trusty-main_20190312 trusty-multiverse_20190312 trusty-restricted_20190312 trusty-universe_20190312

Explanation

• perl -lne: read the input file line by line (-n), remove trailing newlines (-l) and run the script given by -e on each line. The -l also adds a newline to each print call.
• next unless /^\s*\*\s*(\S+)/; : find the name of the repo, so the first stretch of non-whitespace characters (\S+) on a line that starts with 0 or more whitespace characters (^\s*), then a * (\*), and 0 or more whitespace characters again. The longest stretch of non-whitespace after that is what we want. If this line doesn't match this regex, the next will move us onto the next line.
• $n=$1 : save what was captured by the match above (the (\S+) in parentheses, $1) as $n.
• @k=(/\{.+?:\s*\[(.+?)\]/g): find all cases where we have a {, any other characters and then a :, followed by whitespace and a [ and capture anything between the [ and the ]. Save all matching strings in the array @k.
• print "$n @k" : finally, print the name of the repo, the $n, and the array @k from above.

If you prefer to have the square brackets included, you can use:

$ perl -lne 'next unless /^\s*\*\s*(\S+)/; $n=$1; @k=(/\{.+?:\s*(\[.+?\])/g); print "$n @k"' file 
test_repo_one/xenial [xenial-main_20190311] [xenial-multiverse_20190311] [xenial-restricted_20190311] [xenial-universe_20190311]
test_repo_one/xenial-security [xenial-security-main_20190311] [xenial-security-multiverse_20190311] [xenial-security-restricted_20190311] [xenial-security-universe_20190311]
test_repo_two/trusty [trusty-main_20190312] [trusty-multiverse_20190312] [trusty-restricted_20190312] [trusty-universe_20190312]

My awk approach:

$ cat 1.txt 
Published repositories:
 * test_repo_one/xenial [i386,amd64] publishes {main: [xenial-main_20190311]: Snapshot from mirror [xenial-main]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {multiverse: [xenial-multiverse_20190311]: Snapshot from mirror [xenial-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {restricted: [xenial-restricted_20190311]: Snapshot from mirror [xenial-restricted]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}, {universe: [xenial-universe_20190311]: Snapshot from mirror [xenial-universe]: http//gb.archive.ubuntu.com/ubuntu/ xenial [src]}
 * test_repo_one/xenial-security [i386,amd64] publishes {main: [xenial-security-main_20190311]: Snapshot from mirror [xenial-security-main]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {multiverse: [xenial-security-multiverse_20190311]: Snapshot from mirror [xenial-security-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {restricted: [xenial-security-restricted_20190311]: Snapshot from mirror [xenial-security-restricted]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}, {universe: [xenial-security-universe_20190311]: Snapshot from mirror [xenial-security-universe]: http//gb.archive.ubuntu.com/ubuntu/ xenial-security[src]}
 * test_repo_two/trusty [i386,amd64] publishes {main: [trusty-main_20190312]: Snapshot from mirror [trusty-main]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {multiverse: [trusty-multiverse_20190312]: Snapshot from mirror [trusty-multiverse]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {restricted: [trusty-restricted_20190312]: Snapshot from mirror [trusty-restricted]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}, {universe: [trusty-universe_20190312]: Snapshot from mirror [trusty-universe]: http//gb.archive.ubuntu.com/ubuntu/ trusty[src]}

$ awk '$1=="*"{split ($0, a, /:/); print $2 a[2] a[5] a[8] a[11]}' 1.txt 
test_repo_one/xenial [xenial-main_20190311] [xenial-multiverse_20190311] [xenial-restricted_20190311] [xenial-universe_20190311]
test_repo_one/xenial-security [xenial-security-main_20190311] [xenial-security-multiverse_20190311] [xenial-security-restricted_20190311] [xenial-security-universe_20190311]
test_repo_two/trusty [trusty-main_20190312] [trusty-multiverse_20190312] [trusty-restricted_20190312] [trusty-universe_20190312]