Did you also delete the steam user data when reinstalling it? Regardless, I found a Github issue that looks very similar to yours. Apparently this was caused by a beta update? But this was about 4 months ago? Weird.
Anyway, the suggested fix was to first reset steam with flatpak run com.valvesoftware.Steam --resetAnd then opt out of any potential beta: com.valvesoftware.Steam -clearbeta
Not sure if this really is the same issue, but it’s definitely worth a try.
Edit: Seems like on some systems, removing the package xdg-desktop-portal-gnome also fixed it. Don’t know if it also applies to the flatpak, but just try it. Just remember to install the package again if it doesn’t fix it. It may be needed for some other things.