I know this is an old thread, but did you ever get this working? I have the exact same setup as you and am looking to get it hooked into home assistant.
See the below post for working yaml for esphome, most these things require 6W so probably going with the below for esphome. Problem is heat because of where the box hooked to the fireplace is due to heat for the relay. I thought RF was the future of remotes, glad 8 was wrong for the most part.
Relay Module WiFi 4‑Channel ESP8266 Development Board Voltage Monitoring Relay Electronic Components Industrial Parts for Wireless Control DC7‑12V/5V USB https://a.co/d/aAysyIc