So there indeed is a field called "Altitude" in the EXIF data, and I've always assumed it's from the drone itself via GPS, along with the coordinates (i.e. absolute height from sea level). And at least in Lightroom it's reported as meters, with the unit.
However, now that I took a closer look at some of the recorded altitude values, they seem to be all over the place. I have several photos showing negative altitude in double digit meters – while literally flying above sea. And in many other cases the values don't seem to correspond to the height I'm able to eyeball from the photos. Not sure if there's just something wrong in my particular unit regarding the EXIF-recorded height or is this a common behaviour. In any case the altitude shown during flight and what is in the flight logs seem to be pretty much spot-on correct, so with some manual labor you should be able to get the actual heigth for any photo. Really wish the EXIF data was correct too though…