C-wire setup for boiler for a smart thermostat

[Fee]

I want to install a smart thermostat for one of my boiler zones. My thermostat doesn't have a C-wire and has two wires hooked up to the R terminal and two wires hooked up to the W/Aux terminal. It looks like installing an adapter would be the best option, but I am not sure my system is compatible. I see reviews for the Honeywell adapter can be used with boilers, but the instrstuctions say you can't use it if you don't have a G and Y wire . Can anyone verify that a C wire adapter would work in my situation?

- Yellow/black wires = R and Red/Green = W/Aux