[processor/logdeduplication] Review processor shutdown behaviour

[MikeGoldsmith]

This is a tracking issue for reviewing the shutdown behaviour in the new logdeduplication processor.

          Is all of this extraneous? Create a local done channel, listen for it to close, but defer closing it?

The only thing somewhat useful this might be doing is returning ctx.Err() in the case where the passed in context is canceled while we're shutting down. I'm not convinced that's useful though and not aware of any other cases where we do that in Shutdown.

Originally posted by @djaglowski in #34465 (comment)

[codeboten]

Thanks for volunteering to take this on @MikeGoldsmith

[github-actions]

Pinging code owners for processor/logdeduplication: @BinaryFissionGames @MikeGoldsmith @djaglowski. See Adding Labels via Comments if you do not have permissions to add labels yourself.

[MikeGoldsmith]

Fixed in #34563

[github-actions]

Pinging code owners for processor/logdedup: @BinaryFissionGames @MikeGoldsmith @djaglowski. See Adding Labels via Comments if you do not have permissions to add labels yourself.

[crobert-1]

Sorry for the ping, I'm updating labels to the correct name of the processor to properly show up in queries for this component.