The have_seen_event cache is not invalidated when we persist an event.

This is evident when a /messages request triggers a /backfill and it claims that we have the same missing state and auth events each time we _process_pulled_event from the backfill response even though we just fetched and persisted those same state and auth events from the previous event we processed.

I see that we have one spot in Synapse where we invalidate the have_seen_event cache (besides when we purge a room) but if I add a log line to _invalidate_caches_for_event, it never runs in my Complement tests. Does this have a bug where the CacheInvalidationWorkerStore stuff never runs in monolith mode?

Discovered while trying to make Synapse fast enough for this MSC2716 test for importing many batches. As an example, disabling the have_seen_event cache saves 10 seconds for each /messages request in that MSC2716 Complement test because we're not making as many federation requests for /state (speeding up have_seen_event itself is related to #13625)

But this will also make /messages faster in general so we can include it in the faster /messages milestone.

Dev notes

have_seen_event cache originally added in #9953