iPad is possessed

The initial suggested exorcism is to try a forced restart:

https://support.apple.com/en-us/HT210631

If this does not resolve the problem, then either a visit to the Genius Bar at your local Apple Store is recommended - or perhaps seek assistance directly from Apple Support. The Contact Support link can be found at top right of this page.

I hope you find this to be helpful in banishing your daemons.

That seems a bad digitizer; the part of the screen that detects presses and swipes.

If a restart, and failing that then a backup-and-wipe-and-reload-and-restore doesn’t cure this, you’re headed for a hardware repair.

The hardware repair will mean you need a backup anyway, so the attempted restore isn’t that much more effort.

And I’d suspect you’re probably headed for a repair, as I’ve met some bad digitizers.