Being the COVID restrictions so tight in Italy I did not manage to visit many Dive Centers in Sicily during the last few months :-(
but I'm keeping trak of them here:
Diving Centers in Sicily – Diving Laubfrosch
The list is not complete and it gets updated whenever I get to know more of them.
If you want to know who does provide BP/W for customers ... fromt the linked list I'd say: none!
A few instructors/guides use tech gear constantly though, namely Saracen, Centrosubatlantis, Blunauta. I think I will ask them directly if they have the equipment for rent too. Will let you know. Do you need some specific info too?