Under settings, display you can turn off auto lock and the screen lock/unlock. If those were turned off or the auto lock time set to never, that could be part of it.
THat said, I just set mine to auto lock never and have the screen lock/unlock (using the cover to wake it) turned off and my power button still turned my ipad off.
I’ve never played with assistive touch though, so I wonder if that could be part of it?
Have you tried to turn off assistive touch, then make sure those other settings are where you want them to be?
A very tedious thing to do could be to restore it back to factory defaults and see if the issue replicates. Back it up first, then restore it back to factory defaults. If the issue keeps going there’s something wrong, if not then it’s something in the settings. THe downside, it takes a bit and can be very time consuming to try that out.