Okay, well then we’ll need to investigate further.
On one page I found a set of rm commands for resetting Steam issues and adapted it to the Flatpak version.
While these commands will delete most of the steam stuff, just in case you didn’t know, for any flatpak you can run flatpak uninstall --delete-data to delete all user data for uninstalled apps. Or, if you don’t want to uninstall the app first, just deleting ~/.var/app/the app you want to delete the data of will also do the trick. That, just as a small side note.
Resetting it like this seems to work a bit. The Steam interface started up one time and after logging in and restarting it, it now does the same thing as before.
That’s something at least. Why don’t we try something? Maybe the beta version will fix it? When you have the steam client open, try switching to the beta version of it. You can do that by opening the steam settings, go to interface and select the beta. If that also doesn’t work, try launching it with -no-cef-sandbox, as that also fixed it for some people.