The agg stage would have the format:

{
  $_internalGlobalIndexTransform: {
    indexCollectionUUID: <uuid of global index from index catalog>
    recipientShardId: <>,
  }
}

The agg stage performs 2 tasks:
1. Filters out documents that do not belong to recipientShardId.
2. Transforms the input document into the following format:

{
  _id: <object containing fields with index key value pairs>,
  documentKey: <union of _id and shard key values of source collection, where _id is first element>
}

The _id of the output document is the index value representation based on the index key spec specified by indexCollectionUUID.