This is follow up work to #70330.

When the server shuts down, this is indicated to the accumulator via the context.Done() channel.
When this happens, the accumulator consumes at most 1 of the log messages buffered so far on messageCh. If there were more messages there, they get lost.

The code should be updated to loop over messageCh until the read blocks.

(Also, we would want the shutdown to be signalled to the logging system as late as possible. Perhaps a different context cancellation should be used, that is only called very late in the server startup sequence).

Jira issue: CRDB-11163