…timestamp_to_event_endpoint` test flake. Make sure we backfill the closest local event if it's an `outlier` so we can use it with `/context` and paginate `/messages` from this point. Previously we only did this for a remote event.

Fix  #13944

Why did this fail before? Why was it flakey?
====================================================

Sleuthing the server logs on the CI failure, it looks like `hs2:/timestamp_to_event` found `$NP6-oU7mIFVyhtKfGvfrEQX949hQX-T-gvuauG6eurU` as an `outlier` event locally. Then when we went and asked for it via `/context`, since it's an `outlier`, it was filtered out of the results -> `You don't have permission to access that event.`

This is reproducible when `sync_partial_state` races and persists `$NP6-oU7mIFVyhtKfGvfrEQX949hQX-T-gvuauG6eurU` as an `outlier` before we evaluate `get_event_for_timestamp(...)`. To consistently reproduce locally, just add a delay at the [start of `get_event_for_timestamp(...)`](https://github.com/matrix-org/synapse/blob/cb20b885cb4bd1648581dd043a184d86fc8c7a00/synapse/handlers/room.py#L1470-L1496) so it always runs after `sync_partial_state` completes.

```py
from twisted.internet import task as twisted_task
d = twisted_task.deferLater(self.hs.get_reactor(), 3.5)
await d
```

In a run where it passes, on `hs2`, `get_event_for_timestamp(...)` finds a different event locally which is next to a gap and we request from a closer one from `hs1` which gets backfilled. And since the backfilled event is not an `outlier`, it's returned as expected during `/context`.

Future changes
==========================

In a future PR, it would be nice if `/context` would just backfill the event for us. This would also help with #3848

See #14096 (comment)

…ate-complement-backfill-test-flake

…tliers

See:

 - #14096 (comment)
 - #14096 (comment)

…ate-complement-backfill-test-flake

…n when not logging at that severity

See #14096 (comment)

Co-authored-by: Erik Johnston <[email protected]>