HomeBridge has a plugin for simple relay-plus-sensor configurations like this. One GPIO pin is a relay trigger and the other is a sensor pin.
It's important to insure that the Pi is isolated from from the opener. To that end, a reed relay controlled by an N MOSFET is sufficient for a garage door button.
A typical magnetic sensor is a switch closing, not unlike a relay. While it's sufficient to simply use a pull-up and switch it against ground, it's slightly safer to do something like MIDI - set up an opto isolator to capture the switch closing and translate that into a logic level for the Pi.
On the software side, I've used HomeBridge to talk to the service behind a Chamberlain gateway, and that works pretty well (EDIT: well, it did until this week. Check out the logs). Our new home comes with a Genie garage door opener, and I was considering buying their Aladdin internet connection gizmo. The problem with that, though, is that it's essentially a relay and a sensor. So it's really not any better than just doing it this way, but you're paying extra and adding an extra Internet layer for little gain.