Unless I’m misunderstanding, I don’t think this idea will work.

In most programmable thermostats, the “R” terminal on the t-stat is both the source voltage to power the thermostat and also redistributes that same power to each energized output.

Using a transformer to step down the 120V signal voltage will power the 24V thermostat but then the energized outputs will also be 24V back to the furnace. Each thermostat output would individually then need to be transformed back to 120V since the current controls internal to the furnace are looking for a 120V signal.

Also, some thermostats use triacs instead of relays for energizing the outputs. You could potentially damage a thermostat if you put 120V on a 24V rated triac circuit.