Optimize `/backfill` to respond faster

This issue has been migrated from [#15653](https://github.com/matrix-org/synapse/issues/15653).

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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(...)`](https://github.com/matrix-org/synapse/blob/1903c7e5edccc86f6d28aed33dc2995b43d941b7/synapse/storage/databases/main/event_federation.py#L1402-L1533): 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:
- https://github.com/matrix-org/synapse/pull/14527
- https://github.com/matrix-org/synapse/pull/15617

3.45s `/backfill?limit=100` request

934ms `/backfill?limit=100` request

Start by profiling the /backfill?limit=100 entry point and reading get_backfill_events(...) in synapse/storage/databases/main/event_federation.py, then investigate the listed get_current_state, get_filtered_current_state_ids, is_host_joined, and _get_state_groups_from_groups(...) calls. Done means showing that /backfill responds faster than the reported 3.45s and 934ms examples while preserving its existing behavior.

Written by the indexing model from the issue text.