Unfortunately the container breaks certain extensions (e.g. keepassxc-browser). And that's ignoring the fact that, at least on my machine, the flatpak fonts look terrible for some reason and I often run into issues with the Gnome theme not being properly inherited.
Try flatseal and see if you can tweak the permissions.
Re: terrible look, I face the same thing with Telegram (the mouse reverts to whatever is the default in Qt and ignores the system settings). I haven't been able to fix that.
When installing distro, I usually remove some included packages and install newest Firefox, LibreOffice, Gimp, Inkscape etc from Flatpak, because Flatpak has newest versions. Many packages do not update .deb anymore, they have moved to Flatpak.
I uninstalled the snap, then did apt install firefox, worked fine. In principle I am all in favor of more sandboxing for my browser, but when I opened FF on the machine I'd upgraded to Impish, it didn't import anything, open tabs, bookmarks, nada. Not what I'd call friendly onboarding...
Possibly getting Firefox from Debian Sid (unstable). Will require some advanced apt configuration to make sure that nothing else accidentally comes from sid, and might break or require further apt configuration changes if it starts requiring library versions that aren't in Ubuntu.
I use Ubuntu and I sometimes install Debian Sid packages by downloading them in a browser and installing them with dpkg.
The deb package remains available in the archive and will continue receiving updates for the lifetime of Ubuntu 21.10.