federation catchup is slow and network-heavy

[matrixbot]

This issue has been migrated from #9492.

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If a remote HS takes a long time to process a transaction (perhaps because of #9490), then we will enter "catchup mode" for that homeserver. In this mode, we only ever send the most recent event per room, which means that the remote homeserver has to backfill for any intermediate events, which is, comparatively very slow (and may require calling /state_ids, see matrix-org/synapse#7893 and matrix-org/synapse#6597).

So, we have a homeserver which is struggling to keep up, and we are making its life even harder by only sending it a subset of the traffic in the room.

I'm not at all sure why we do this. Shouldn't we send all the events that the remote server hasn't received (up to a limit)?