Part of https://github.com/element-hq/synapse/issues/18905
Lints for ensuring we use `Clock.call_later` instead of
`reactor.callLater`, etc are coming in
https://github.com/element-hq/synapse/pull/18944
### Testing strategy
1. Configure Synapse to log at the `DEBUG` level
1. Start Synapse: `poetry run synapse_homeserver --config-path
homeserver.yaml`
1. Wait 10 seconds for the [database profiling
loop](9cc4001778/synapse/storage/database.py (L711))
to execute
1. Notice the logcontext being used for the `Total database time` log
line
Before (`sentinel`):
```
2025-09-10 16:36:58,651 - synapse.storage.TIME - 707 - DEBUG - sentinel - Total database time: 0.646% {room_forgetter_stream_pos(2): 0.131%, reap_monthly_active_users(1): 0.083%, get_device_change_last_converted_pos(1): 0.078%}
```
After (`looping_call`):
```
2025-09-10 16:36:58,651 - synapse.storage.TIME - 707 - DEBUG - looping_call - Total database time: 0.646% {room_forgetter_stream_pos(2): 0.131%, reap_monthly_active_users(1): 0.083%, get_device_change_last_converted_pos(1): 0.078%}
```
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