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.

It sounds as if you're interested in the extreme DIY, but: my solution was to buy cheap ZWave tilt sensors.

I've been thinking about this recently too!

I kind of have a very crude version of this, by simply mounting my garage door tilt sensor as high up on the door as I could. Since it would go horizontal along with the very first section of the door, it triggers as soon as the door is open about 1/5 of the way.

Response isn't very fast, though, so if I wanted more precise control I was thinking about building 3 ESP distance/ultrasonic sensors mounted to the ceiling pointed downwards, one at the end of the track, one about 1/4 of the way from the end of the track, and one at the start (where the top of the door stops when it's completely open).

So the sensors would detect in order of sensors triggered, "closed -> cracked -> slightly open/ing -> open".

Tracking the previous state of the door in a variable would let me know the direction the door is moving as the sensors get triggered too.

I installed an ultrasonic Sensor at the lowest segment of the garage door. It mostly does it's job, though it is unreliable when the door is fully open, as the sensor tilts towards the open end and the distance is then too long. Also someone standing in the opening might block the sensor.

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.