Investigate reducing INFO logging impact on docker

[matrixbot]

This issue has been migrated from #8023.

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The context here is that we'd like to change our default logging to a) not take up so much room and b) use less disk I/O. For installations where we write logs to the disk we can do things like use buffered logging (#8018) and/or keeping INFO logging for a shorter period of time (#8019). Unfortunately, for docker Synapse logs to stderr which is then picked up by the docker daemon, making it hard/impossible to do the same sort of things we did when writing to disk.

Some potential ideas:

• Log WARN to stderr, INFO to a mounted volume
• Investigate if we can fiddle with e.g. syslog to make it to the write thing and then document that, etc