I just connected my garage door opener to Home Assistant by taking apart a paired remote and wiring the button to a Zigbee relay. They can't stop me, no part of this is connected to their cloud. In any case, smart home stuff should never rely on the cloud.
This is genius. As someone who is familiar-enough with minor electronics to fuck something up, but not confident enough to look at this photo and go for it—what am I trying to learn here? What are the terms I'm trying to google to figure out how to connect <electronic board> to <electronic board> via <wires>?
One of the articles on this mentioned "ratgdo" as a simple board to do most of the "make a button wirelessly available to homeassistant", I haven't tried it but searching on it gets you a lot of reasonably specific articles and videos.
The pictured solution is very easy and comes with directions (ratgdo).
However, if even that is too much you can make a Switchbot do almost anything. It's just an actuator that pokes buttons and is a premade product with a shell rather than a DIY thingy.
https://i.imgur.com/lNOXdhe.jpg
If you have a Chamberlain garage door opener and looking to connect it to HA you can do this too.