Screen

I’ll assume there is no protective case and no screen protective film installed here.

How to get it to shut down? It’ll shut off by itself when the battery is exhausted.

What to do? Use the Get Support link in the upper right of this webpage, and discuss your options with Apple.

You might be able to enable Reachability, which is an accessibility option on the Pro Max models. This allows you to swipe down off the bottom of the display, and drag the upper part of the display down to where you might be able to access the controls. If you can get Reachability enabled, which might be possible with Siri.

Reach the top of the iPhone screen with one hand - Apple Support

Use accessibility features with Siri on iPhone - Apple Support (CA)

But this iPhone needs a repair.

Force restart doesn't require use of the touchscreen. But you might not be able to enter your passcode when it restarts.

Force restart iPhone - Apple Support