Stop processing updates more quickly on shutdown

As we discovered in SOLR-8129, existing update streams can continue to be processed for some time when the CoreContainer is being shut down. If this node is the leader, updates can continue to flow to replicas over the existing streaming client (although new or idle clients won't be allowed to send anything).

This can cause large reorders of updates and shard inconsistencies that we can't detect with the current PeerSync mechanism.