Related to https://github.com/element-hq/synapse/issues/18905
These fixes were split off from
https://github.com/element-hq/synapse/pull/18828 where @devonh was
seeing some test failures because `timeout_deferred(...)` is being
updated to use `Clock` utilities instead of raw `reactor` methods. This
test was failing in that branch/PR until we made this new version that
handles the logcontexts properly.
While the previous version of this test does pass on `develop`, it was
using what appears completely wrong assertions, assumptions, and bad
patterns to make it happen (see diff comments below)
---
Test originally introduced in https://github.com/matrix-org/synapse/pull/4407