This PR switches several conditions regarding room access rules to check against the status of the room's inclusion in the public room list instead of its join rules.
The code includes a snapshot of https://github.com/matrix-org/synapse/pull/8292, which will likely change in time and need merging in again.
Fixes https://github.com/matrix-org/synapse/issues/7683
Broke in: #7649
We had a `yield` acting on a coroutine. To be fair this one is a bit difficult to notice as there's a function in the middle that just passes the coroutine along.