Prediction: you will spend 2 hours of fruitless effort trying to get
things loose before you give up in despair and a) call a plumber to
replace the entire antique assembly with new, or b) replace the faucet
set yourself. Check for access behind the fittings before proceeding.
With luck there may be an access panel. Accept the inevitable and save
your sanity.

No access. It's back to back with another tub in the other bathroom. And
full ceramic tile on both. A pro may have better tools to get the handles
off but even he/she isn't going to be able to replace the valves and piping
without ripping open the wall if in fact that's what it comes down to.
That's too much trouble just to cure some drips especially when you
consider that logically one would want to replace the piping and valves for
the other side while the wall is open. That's not really justified to save
a few drops.