We have logic which is guarded behind the (currently disabled by default and untested) FeatureFlagUpdateDocumentShardKeyUsingTransactionApi to handle changing a document's owning shard with the internal transaction API.

Once we move toward testing and enabling that flag, this logic will need to be updated to work for the bulkWrite command as well. (SERVER-72793 covers updating the legacy WCOS logic to work for bulkWrite.)