Currently, we only have `session_id` in the `handle_client` span, so
it's really hard to track the whole connection path in the logs.
Especially if error occurs.
This commit adds `session_id` explicitly into several other messages.
This could be a bit too verbose, but I've tried several combinations of
`span.in_scope()` and `instrument` and it didn't play well, because all
related messages are in the different contexts.
87b02c91c6