FWIW I've run a mica window geiger cointer for hours in front of my tubes and been completely unable ti measure any radiation above ambient. At some point I will do it with a large scintillator, but already it's pretty clear that those X-rays are very soft indeed.

The glass where the image is displayed is quite thick, and leaded for just this reason. There is also a protection circuit that will shut down the whole set if the voltage were to increase enough to risk xrays that can't be contained.