UPDATE: Okay, so I think I made some great progress! Software Update popped up with that reminder to upgrade to Ubuntu 22.04, and I had been considering it seriously now. So I decided to go for it. It took less than 30 minutes, a reboot, and done. Most things are the same as far as I can tell. The Show Applications function is different, icons are smaller and not in alphabetical order like they were before, but maybe I can adjust those things in Settings. Wallpapers were replaced with new ones also. I might have saved my favorite one if I knew that.
It actually updated to Ubuntu 22.04.4 LTS (rather than 22.04.3 LTS). So then I tried the Proton VPN install. Similar issue at first, with install error messages in Terminal. So I did “cd Downloads” (where the package is located) and then tried the script again and … success! Installed and using the VPN right now. It’s possible that directory change would have done the trick without the distro version upgrade, but say-lah-vee. 
It probably was a good idea anyway. Progress, y’know.
Note: When I first connected Proton VPN, I got the list of servers, clicked on one, and it briefly did that “empty window with the chosen server” trick, but then reverted back to the full server list and connected quickly. Similar behavior as when I had the problem connecting in 20.04, but now it actually works! So maybe I did need the 22.04 upgrade after all.
I’ll keep Mullvad VPN in mind though. Seems like maybe it’s the best around, and the price is pretty reasonable.