Ubuntu-MATE 20.04 - missing Network Connections

I have a shiny new Lenovo P14s 2nd gen ( installed with dual boot, Win10 and… ) Ubuntu MATE 20.04.2 LTS. And I can't connect by Wi-Fi. For some graphics-related driver issues (a little too shiny new after all for Ubuntu 20.04 it seemed) I did upgrade the kernel to 5.12.4 generic, but this is probably not relevanthere.

I can't see any network connections. Neither in the top panel (where a respective pulldown would sit in the Notification area with the well-known wifi waves-symbol) nor in the control-center (like I do under my old 16.04 machine, where there was a „Network Connections“ with all the nearby Wifi's to choose from) from. Here, it's missing:

(the usual rest is there, but nothing on “Network Connections”...)

I first suspected that also my Wifi adapter might be 'too' new and needs drivers… However I a) installed some drivers follwoing Lenovo documents and b) also plugged in a truly simple (3-4 year-old) USB LogiLink-Wifi adapter – no luck, no wifi connections offered anywhere.

inxi -N says, it's all there!

$> inxi -N
Network:    Device-1: Intel Ethernet I219-V driver: e1000e
            Device-2: Intel driver: iwlwifi
            Device-3: Ralink RT5370 Wireless Adapter type: USB driver: rt2800usb
            Device-4: Lenovo USB3.1 Hub type: USB driver: r8152

…and so does iwconfig. The wlx... one must be the external one (simple plug-in-plug-out test). I am not a driver/hardware expert, but looks to me like both devices are recognized and even operational (even with Bit Rate and Quality measuring under way...)

lo        no wireless extensions.
enp0s31f6  no wireless extensions.
enx083a885b1fdf  no wireless extensions.
wlp9s0    IEEE 802.11  ESSID:"WN-62F2C0"
      Mode:Managed  Frequency:5.54 GHz  Access Point: 7C:<redacted>:C5
      Bit Rate=866.7 Mb/s   Tx-Power=22 dBm
      Retry short limit:7   RTS thr:off   Fragment thr:off
      Power Management:on
      Link Quality=69/70  Signal level=-41 dBm
      Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
      Tx excessive retries:0  Invalid misc:63   Missed beacon:0
docker0   no wireless extensions.
wlx7cdd9017b62f  IEEE 802.11  ESSID:off/any
        Mode:Managed  Access Point: Not-Associated   Tx-Power=20 dBm
        Retry short  long limit:2   RTS thr:off   Fragment thr:off
        Power Management:off

$> dpkg -l | grep -i "network.*manager"

ii libnm0:amd64                          1.22.10-1ubuntu2.2 amd64 GObject-based client library for NetworkManager
ii libproxy1-plugin-networkmanager:amd64 0.4.15-10ubuntu1.2 amd64 automatic proxy configuration management library (Network Manager plugin)
ii network-manager                       1.22.10-1ubuntu2.2 amd64 network management framework (daemon and userspace tools)
ii network-manager-gnome                 1.8.24-1ubuntu3    amd64 network management framework (GNOME frontend)
ii network-manager-openvpn               1.8.12-1           amd64 network management framework (OpenVPN plugin core)
ii network-manager-openvpn-gnome         1.8.12-1           amd64 network management framework (OpenVPN plugin GNOME GUI)
ii network-manager-pptp                  1.2.8-2            amd64 network management framework (PPTP plugin core)
ii network-manager-pptp-gnome            1.2.8-2            amd64 network management framework (PPTP plugin GNOME GUI)

I am really clueless... thank you for your help!