@teresa_athome sudo apt-get update gave me:

Ign:1 http://dl.google.com/linux/chrome-remote-desktop/deb stable InRelease
Hit:2 http://dl.google.com/linux/chrome-remote-desktop/deb stable Release
Hit:3 https://dl.google.com/linux/chrome/deb stable InRelease
Hit:5 https://developer.download.nvidia.com/compute/cuda/repos/ubuntu2204/x86_64 InRelease
Hit:6 http://us.archive.ubuntu.com/ubuntu jammy InRelease
Hit:7 https://linux.teamviewer.com/deb stable InRelease
Get:8 https://download.mono-project.com/repo/ubuntu stable-focal InRelease [4,416 B]
Get:9 http://us.archive.ubuntu.com/ubuntu jammy-updates InRelease [128 kB]
Get:10 http://security.ubuntu.com/ubuntu jammy-security InRelease [129 kB]
Hit:11 http://us.archive.ubuntu.com/ubuntu jammy-backports InRelease
Hit:12 https://ppa.launchpadcontent.net/mozillateam/ppa/ubuntu jammy InRelease
Hit:13 https://hub-dist.unity3d.com/artifactory/hub-debian-prod-local stable InRelease
Fetched 261 kB in 1s (175 kB/s)
Reading package lists... Done
N: Skipping acquire of configured file 'main/binary-i386/Packages' as repository 'https://download.mono-project.com/repo/ubuntu stable-focal InRelease' doesn't support architecture 'i386'

... but then when I ran the GUI Software Updater, I again got "The package system is broken".

/var/log/apt/term.log appears to contain a series of "Preparing to unpack" / "Unpacking" lines, but no error messages. (I can paste the whole file if it would help.")