Fix a long-standing bug where a batch of user directory changes would be
silently dropped if the server left a room early in the batch.

* Pull out `wait_for_background_update` in tests

Co-authored-by: Patrick Cloke <clokep@users.noreply.github.com>
Co-authored-by: Richard van der Hoff <1389908+richvdh@users.noreply.github.com>