Homepage (https://github.com/gethomepage/homepage) works fairly well for that use case imho.

If you're running it on a separate server you would have to expose the docker API to it, which you might not want to do. It might be easier to just run it on the same server and proxy it from the bps.

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.