text: Raw search: https://nominatim.openstreetmap.org/search?q=empress%20dock%20victoria&format=json&polygon=1&namedetails=1 doesn't have the operator
  
  but https://nominatim.openstreetmap.org/search?q=victoria+harbour+ferry&format=json&namedetails=1&limit=100 does in fact have the operator for some of the terminals - but as you mentioned it doesn't include the one you're seeking. I'm not sure why, I even increased the limit and it still doesn't include the Empress Dock among the results.
  
  see https://nominatim.openstreetmap.org/details.php?place_id=16751979, it doesn't list operator. but https://nominatim.openstreetmap.org/details.php?place_id=3601277 does. This must be the key somehow.