I've been running LTS versions of Ubuntu (Kubuntu 14.04, Ubuntu MATE 16.04, and now back to Kubuntu 20.04) for several years, and I've never had a successful "upgrade" vs. installing everything from scratch -- the latter process usually takes me a full day, sometimes running well into a second (there goes a weekend), as opposed to an hour or two for a proper upgrade to run and keep my installed applications.
I use a couple PPA sources (one for Java, for instance, and one for SeaMonkey browser/suite), and have one major SNAP application (GIMP). It's been my understanding that SNAP installs are independent of the system upgrade process, and I'm aware the upgrader will disable the PPA entries and I'll have to re-enable them, possibly with version changes, after upgrading is complete.
However, in the past, I've never succeeded in upgrading from one LTS version directly to the next. This was because, at first, I was advised against attempting to upgrade from 14.04 to 16.04 (and I switched flavors because at the time I disliked the changes in Plasma 5). I attempted upgrade from MATE 16.04 to MATE 18.04, and the upgrade failed; since I was stuck with clean install anyway, I switched back to Kubuntu, and since this was in mid-2020, used 20.04.
With 22.04 coming out very soon, and the point release due over the summer, I'd like to maximize my chances of being able to upgrade, as opposed to reinstalling. Not running PPA software is not really an option, but I'm open to other recommendations (and we have some time, it's several months until the point release).
It doesn't matter whether you're migrating from LTS-to-LTS or among 6-month releases. The principles are the same. Some folks have problems with both. Others have no problems at all.
For the highest likelihood of success, it's back to basics:
Keep notes: Write down what you install on top of a release. Write down sources. Write down package names. Write down URLs of instructions. Write down when you installed package XYZ and why. Write down how to restore your data from a backup.
Your notes are your instruction manual to yourself. They should tell you how to rebuild/restore your preferred system from a clean install.
Backups: Backup your data. Backup your configs and customizations -- those are harder, so it's good that you have notes!
Clean up your debs: Before a release-upgrade try to return your system to as close to stock condition as possible. Uninstall any third-party debs you might have bolted on, and comment out their sources. DON'T start a release-upgrade until apt is 100% happy with your packages; release-upgrade rarely fix problems but can easily make those problems worse!
Read your output: During the release-upgrade, pay attention at the beginning and at each prompt. Read them. Then read them again to make sure. Don't accept a "partial upgrade" (that means a failed upgrade!) unless you absolutely must. Better to fail entirely and return to Step 3 to clean out the offending wrong-version debs.
Review your updated sources: Before restoring non-Ubuntu deb sources, check the Ubuntu repositories. Maybe an acceptable version of that software is in Ubuntu now. Or maybe (like Firefox or Chromium) the developers prefer a Snap version now. When enabling non-Ubuntu sources, make sure the deb source is compatible with the new release. Some third-party and PPA sources aren't ready on release day, so check and be patient.
Maybe you don't use that software at all anymore, or perhaps it can wait a week or two until you are likely to use it.
Be Prepared: Disaster never seems to strike when you are fully prepared for it. Exploit that! A newly-made LiveUSB in your pocket. Notes printed out (or on your phone) that includes how to access your remote data backup. Mains power and a stable network connection. Preparation turns a multi-day screaming crisis into a single rather-dull evening punctuated by a nice sandwich.
Yup, the basics that you already know: Flossing keeps your teeth healthy. Proper tire pressure improves your car's fuel economy. Wear a clean shirt to Grandma's house. No magic about it at all.