in our car it remained when I toggled the HUD on and off. I drove the car this morning during a rainstorm with alternating patches of heavy rain and clear blue sky. The spot remained although it did vary in intensity with changes in sunlight levels.
That crossed my mind after I dropped the car off at the PPF shop. I'll check for that when we get the car back. I would hope that the prep team would have removed any film that might have been there, but they missed a couple of other things, such as an air vent that blows defroster air up the driver's side A pillar that was sticking up. (I was able to pop it back in place myself and hope it holds.)
There is a brightness slider, but I did not notice any difference in the HUD image brightness as I moved it back and forth. It also had no effect on the reflection.