Rework SyncerRegistry tests to fix flakes

Created by: mrnugget

This splits up the previous test into two and removes the background goroutine when testing the syncing of code hosts.

This should fix https://github.com/sourcegraph/sourcegraph/issues/24508

I ran all the tests in the syncer package with -race -count=1000 and I also can't see any potential race conditions anymore.