It looks like that problem is fixed with Flatpak override and not installing the Flatpak with root?

This is also probably because the Signal Flatpak is community developed on Flathub from Signal's .deb, they're not building Signal with Flatpak in mind. Mozilla provides an official Flatpak release of Firefox.

I'm sure official Flatpaks do better on average, but that narrows the selection a lot. And most third-party packagers raise my suspicions in a way that, say, the Debian packaging team does not. You should see my eyebrows go up when I cruise dockerhub!

I don't know what the right answer here is, but for me it's not Flatpaks or Snaps. Trusting the packager (and the org behind the package system) is a huge part of it. I breathe a sigh of relief every time I see the software I need is in Debian's repos, even if that means they may not be optimally sandboxed.