How about getting the gocontrol/linear gd00z-4 (it is a Z Wave device) garage door opener to work on the ring system. My current system (not Ring) allows me to operate my garage door with Alexa or my alarm app.
File it under door locks. Unlock=Open, Lock=Close tilt sensor alerts the status of the door.
Since this is a DIY system, this option for controlling a garage door is super simple to install and works with non-smart garage doors.