Fix https://github.com/matrix-org/synapse/issues/15618
### Before
```
2023-05-17 22:51:36-0500 [-] 2023-05-17 22:51:36,889 - synapse.server - 338 - INFO - sentinel - Finished setting up.
```
### After
```
2023-05-19 18:16:20-0500 [-] synapse.server - 338 - INFO - sentinel - Finished setting up.
```
### Dev notes
The `Twisted.Logger` controls the `2023-05-19 18:16:20-0500 [-]` prefix, see : [`twisted/twisted` -> `src/twisted/logger/_format.py#L362-L374`](34b161e66b/src/twisted/logger/_format.py (L362-L374))
And we delegate our logs to the Twisted Logger for the tests which puts it in `_trial_temp/test.log`
1903c7e5ed