The Logging in integration tests is problematic

Nobody has claimed this yet.

1. We have far too many irrelevant calls to `LogService.error` from the matrix-bot-sdk MatrixClient for things that are expected ie getting a 404 when checking for the existence of a room alias or querying state events. This is causing a sort of alarm fatigue and makes it harder to look for the causes of problems in a full run (`yarn test:integration`).

2. Mocha writes to the output stream in a completely inconsistent order to `LogService`. it can make the logs from `MatrixClient` or other components appear as though they are a result of a calls from a different test than what Mocha says has failed or has started running. Not sure if this is something from Mocha not awaiting test callbacks or something else.

Start by running `yarn test:integration` and observing the interaction between Mocha output and `LogService`. Inspect the MatrixClient calls that emit `LogService.error` for expected 404 responses, along with the integration-test setup that controls output. Done means expected calls no longer create misleading errors and test logs preserve useful test context.

Written by the indexing model from the issue text.