Optimize /backfill to respond faster #15653

Since /backfill is a big part of /messages performance, optimizing /backfill would help other servers respond to our /backfill requests faster which means we can respond to /messages faster.

From the examples below, it seems like we have these obvious opportunities to improve:

• get_backfill_events(...): Seems like a pretty slow query that we could probably turn into a recursive query.
• get_current_state -> get_filtered_current_state_ids: Takes ~200ms
• is_host_joined: uncached call took ~200ms
• _get_state_groups_from_groups(...): A known slow thing
  • Previous optimizations:
    • Optimize filter_events_for_client for faster /messages - v2 #14527
    • Re-use work of getting state for a given state_group (_get_state_groups_from_groups) #15617

3.45s /backfill?limit=100 request

934ms /backfill?limit=100 request