You need the exact right version that matches your actual graphics driver. So flatpak takes care of installing the matching drivers inside the sandbox.
Do you? I've often seen this repeated but at some point I tried a cutting edge chroot on an extremely (ie multiple years) out of date device and opengl seemed to work. It surprised me but then I don't know much about how mesa works under the hood.
this is horrifying, and contrary to the very notion of what a "driver" should be
To be fair the graphics APIs are provided as libraries with as much as possible done in userspace. Sandboxing that without any coupling at all would likely require either new kernel APIs or highly questionable virtual memory shenanigans.