Android and iOS apps with their modern robust sandboxes can still see quite a lot about their OS, e.g. [1] and [2]. This makes me wonder that, if a Flatpak has no permissions (or its permissions are removed with flatpak override) except for necessary ones (e.g. Wayland), what can it see about its distro.
I believe they can read the clipboard arbitrarily, but not sure about anything beyond that (assuming a DE that protects screencopy).