Let’s be clear about something. There were power thermostats. There may still be. There were also things that were switches, without thermostat elements, Like a Off-Low-High power mode switch.

What type you have shown is not clear to me.

If you have a professional look at what you have, they could bring considerable information.

If it does not work the way you want it to, then they can tell you better how to achieve your goals.

A smart thermostat and interface module ( power relay ) make almost any level of control possible.

Edit, addition.. I think you have a line voltage control element, so use great caution⚡️⚡️⚡️