If you have access to any of the rotating parts a hall effect rotary encoder could do what you need. Stick a magnet to the rotating axle of the motor, the sensor next to it and you can encode the position of your door exactly.

Out of curiosity: what would be an automation that would benefit from knowing if it’s opening or closing?

I’m quite happy with this: https://opensprinkler.com/product/opengarage/ It doesn’t know whether the door is opening but has the benefit of knowing whether or not the car is in the garage when then door is closed.