I monitor my boiler’s burner for runtime (on/off) was a relay powered off the input terminals of the burner. I’ve mentioned it here before, including this thread just the other day.
Once you have the relay, you have a few options you can connect to the contacts on the relay. A door sensor has a reed switch inside which you can replace with a wire to the contacts. Or connect the contacts to the GPIO pins on an ESP device running ESPHome.
A CT clamp and ESP device is probably a more elegant solution, but a bit more fiddly to set up.