Can’t get Home Screen So can’t unlock!

Obviously you really need a new screen; is there a reason you don't replace the screen, thus fixing the touchscreen issue that seems to be keeping you from being able to enter your passcode? The older iPhone OLED screens like yours have come down in price drastically; I was regularly able to find iPhone X screens from $15-$20, and those were actual soft OLED displays, not the LCD conversion crap. Yours will be more expensive since you have the Max, but still quite reasonable.

Anyway, rather than a keyboard, I'd suggest a wired mouse. I'm not all that up on how it works on an Apple product, but on my Android a cursor appears as soon as it's plugged in and I can use the mouse to do anything I otherwise would with a touch screen.