There is no magic to resistive heating controllers - they just turn the power on and off, varying the timings. This makes replacing one off the shelf module with another off the shelf (but HASS compatible) module relatively easy.
The only issue could be if there is a temperature sensor buried under the tiles in grout. It’s probably a standard thermistor, but not something I’ve direct experience of (the Screwfix towel rail heater produces enough warmth).