Clean up some LoggingContext stuff (#7120)

* Pull Sentinel out of LoggingContext

... and drop a few unnecessary references to it

* Factor out LoggingContext.current_context

move `current_context` and `set_context` out to top-level functions.

Mostly this means that I can more easily trace what's actually referring to
LoggingContext, but I think it's generally neater.

* move copy-to-parent into `stop`

this really just makes `start` and `stop` more symetric. It also means that it
behaves correctly if you manually `set_log_context` rather than using the
context manager.

* Replace `LoggingContext.alive` with `finished`

Turn `alive` into `finished` and make it a bit better defined.