I cannot get to the desktop screen on my iPhone 13

If the display doesn't respond to your "swipe up" gesture, and if you're sure that nothing (cover, screen protector, dirt) interferes with your touch screen, try a "forced" restart of your device using these instructions: Put it on charge for at least half an hour, then, keeping it plugged in, use these gestures:

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).

If 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:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.