Unable to delete desktop shortcut on iphone 15 pro

If you have Screen Time enabled, go to Settings/Screen Time/Content & Privacy Restrictions/iTunes & App Store Purchases and change Deleting Apps to Allow.

Then try deleting the app again.

Certain built in apps cannot be deleted→Delete built-in Apple apps from your iPhone, iPad, or Apple Watch - Apple Support

Also, if your iPhone has a work or school account, or is under Mobile Device Management (MDM) supervision, or under Parental Controls the administrator can restrict many features of iOS.