Pro-actively backfill rooms with backward extremities

[MadLittleMods]

Background

Currently, we only backfill when we receive a /messages?dir=b request which means any time you want a message and we don't already have it or there is a gap at the time you're paginating over, you have to wait for the /backfill request in the background before we can finally respond to your initial /messages request.

If we instead first attempt to backfill outstanding backward extremities before a /messages request comes in, we will either have the event in the best case, or recorded some event_failed_pull_attempts and we already be ready to backoff and skip the same event when we try to paginate around it later.

Ideally, we would be able to backfill more than real-time for all of the rooms and eventually catch up with everything possible to retrieve.

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Also relates to Synapse trying to make a Matrix room eventually consistent on its own.

Potential solution

Have a regular background job that picks up recently visited rooms with backward extremity and attempts to backfill those positions.

[MadLittleMods]

Closing in favor of #13576