IPhone 13 Pro Max will not shut off with just power button.

There is no single "power button" on an iPhone 13 Pro Max (or other recent iPhone models). The following is how you turn it off and is not a workaround; it is how it is designed to operate:

From Restart your iPhone - Apple Support

1. Press and hold either volume button and the side button until the power off slider appears.
2. 
3. 
   
4. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
5. To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.

Are you holding the side button while pressing the volume up button? If that’s not working, try a forced restart and then try to power down.

Force restart iPhone - Apple Support