I bet I know what you have. I had the same thing. You have a line voltage thermostat switching on a taco circulator. Don't you?

The best thing you can do to save money is rip that ancient furnace out and replace with a new unit. It will save you a lot more money than a smart thermostat, especially given the price of oil.

However, it can be converted to a 24v by connecting the circulator to a taco zone controller and then using any thermostat you want to switch the input on the controller. You will need a pro to do it though as the aquastat is usually interfaced with the zone controller. I don't exactly remember why though.