It looks like that button is a simple closed contact. You could verify that by shorting the two wires together and seeing if the door opens and closes.
If it is you could use the GoControl GD units or a Meross unit or even a Shelly switch as some have done.
I am able to open and close the garage door from within ZWaveJS2MQTT.
Now I’m trying to figure out how to add a card to home assistant that shows me the state of the garage door and allows me to open it and close it. Could someone point me in the right direction?