From memory, here's how it's supposed to work:
1. replica tells leader it want's to recover
2. leader starts forwarding updates to replica (which the replica buffers since it's in recovery)
3. leader executes a hard commit (so replica can replicate the current index)
4. replica starts replicating index from the last leader commit point
Note that the ordering of #2 and #3 is very important. If we did #3 first and then #2 after, some updates won't make it into the commit and also won't be forwarded to the replica (and that leads to data loss).
Now the issue: even though we do #2 first and #3 after... it's possible to have an unfortunately scheduled update in a different thread that started before we did #2, and doesn't complete until after #3, so that update was not forwarded, and it's also not in the replicated index. The sleep (which should be between steps #2 and #3) is to try and give time for this update to complete and make it into the index.
It occurs to me that the lucene IndexWriter thread stealing (same issue that caused this:
SOLR-6820) could make this much more likely than we would have thought.
One possible alternative is to block updates for a commit of this type (replication commit). Any blocked updates would need to see that they need to be forwarded to the replica too (once they are unblocked) - I don't know if the code is currently written that way.