Am redoing the entire bathroom. Going from ancient three handle
tub/shower set to either a modern Pressure Balance valve or a
Thermostatic valve.

I am not clear on what each type of valve can/cannot do. Both are
suppose to be anti-scalding.

Past problems have been, with an old fashioned design, that water
temperature changes while under the shower head. Hot water source is
a tankless embedded 5 gpm heat exchange coil.

Understand that Pressure Balance will compensate automatically for a
change in water pressure, via hot or via cold ports, when dishwasher
or toilet is put in use.

With regard to Thermostatic valve: How will the above problem be
avoided? Does a Thermostatic valve adjust for a water temperature
(within 3 degrees) change by opening/closing the water inlet ports?
Given that the 5 gpm water heater might be overtaxed, will a
Thermostatic valve be the better choice vs a Pressure Balance valve ?

I do not know which type of valve to select for the installation.

Thoughts.