I can't delete an app from the home screen and/or the App Library

You’re probably either trying to delete an app that is a non-deletable part of iOS, or you have screen time enabled and don’t also have app deletion enabled, or this is a managed iPhone with profiles loaded.

The usual cause:

Settings > Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases > enable app deletion

From Delete apps on your iPhone, iPad, and iPod touch - Apple Support

INSTRUCTIONS: How to Delete and App from iPhone

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1) Tap and hold the app you wish to delete.

2) Select “Remove App” from the pop-up menu.

3) Tap “Delete App”

That’s it. The app has been deleted from your iPhone, Home Screen, and the App Library.

You can reinstall the app at anytime. If you paid for additional features, locate the “Restore Purchase” option within the app.

I hope this helps! 😊

Any apps that can’t be deleted like the Clock, can still be removed from the home screen and eliminate clutter. When you tap and hold the app, the option to hide from home screen will appear. Tap that and the icon will just disappear. This action does not delete the app and it will still appear in the app library.

If you ever want to add it back to your Home Screen, Scroll to the app library, tap and hold the App, and select “Add to Home Screen.”

You still don’t understand the problem or the solution, which is that deleting apps is disabled in Screen Time, and the solution is to enable deleting apps in Screen Time, as Mr Hoffman said.

See this YouTube video from Apple Support. Instead of Move to App Library, you can tap Delete and it will delete the app from the Home Screen and App Library.