A flatpak can name extensions that are mounted into the running container if they're installed.

or are Flatpaks allowed out of their sandboxes

Be careful when thinking of flatpaks as sandboxes. What they confine is (by default) up to the maintainer of each flatpak, and most of the ones I have audited are very permissive.

You can mitigate this somewhat by editing the permissions of each flatpak before running it for the first time, with the command line or a GUI like flatseal. But that only goes so far, since some of the permissions are not fine-grained enough to provide meaningful sandboxing while still allowing games to run. (For example, shared memory and network access.) You might also consider creating a second linux account just for games, and logging in to that account's desktop when installing or running them.

A Flatpak container is better than nothing, and will probably keep you safe from most programming mistakes, but I wouldn't consider it a security/privacy sandbox by any means. If you want that, a hypervisor-based virtual machine would be better.