If you're that nothing (case/cover, screen protector, dirt) interferes with your touch screen (remove any obstacles, if present), and if you used the correct gestures to perform a forced restart of your iPhone 13 as per these instructions: Put it on charge for at least half an hour, then, keeping it plugged in, use these gestures:
In rapid sequence, press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the side (power) button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).
but the issue persists, I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> https://locate.apple.com/choose-country-region . After checking it out, they'll give you all the available options.
Regards
Giulio
(*) You can do it: