Be very careful with these!
This type of faucet was installed in the 1920's & 30's and is not code compliant due to the spout being mounted below the flood rim of the tub.
Parts? Good Luck with that!
You may be able to have stems and seats custom made at
New York Replacement Parts and they have a machine shop where they will custom make a stem to match your sample, if those are the only parts needed.
Of course there probably is not a valve that will isolate the tub and shower so the whole house will be off until it goes back together and is working or, gets replaced....
Blow the repair and the only option is a bathroom remodeling...
The bathtub drain is a cylinder inside the wall that has another cylinder inside of it that raises and lowers to act as a stopper and when water goes over the top of the inside cylinder it is the overflow. This drain is integral to the tub spout and valve...
So yea the remodel job is a new tub, new valve, and redoing the tub drain at a minimum...
I sweat when I get one of these and for good reason...