I really do not know why the explain plan seems to indicate (for count_scan) 0ms (number on the left) while Compass indicates 11ms.
The issue is that without the $facet the FETCH only process 10 documents while all documents are FETCHed for $facet.
Try to move $sort right after the $match.
One hack you could try to use $unionWith something like:
This might avoid FETCH of all documents.