Refactor presence so we can prune user in room caches (#13313)

See #10826 and #10786 for context as to why we had to disable pruning on
those caches.

Now that `get_users_who_share_room_with_user` is called frequently only
for presence, we just need to make calls to it less frequent and then we
can remove the various levels of caching that is going on.