If you definitely need to buy a new unit, then I'm guessing that you will have
to do some "Goggle" searching with search terms such as:
custom recessed "bathroom medicine cabinet"

Even so, finding a custom builder for your requirements may be very difficult
and expensive.

On the other hand, you might let this group know why you want to replace
the unit and you may get some good suggestions for repairing it. I'm guessing
that you could pay $250-$500 for a custom replacement. That can cover a
fair number of repairs and upgrades to your existing cabinet.