Iphone Pro Max 14 How do I delete apps from the library?

First disable the Screen Time Restrictions, if any.

Settings > Screen Time > Contenet And Privacy Restrictions > iTunes & App Store Purchases > Deleting Apps > [Allow]

There are six possibilities

1. Delete an offloaded App
2. Delete an App from the Home Screen
3. Remove an App from the Home Screen - Will be placed in the App Library
4. Delete an App from the App Library
5. Delete an inbuilt App - Not feasible
6. Delete an inbuilt App with one feature - You do not get any options either (e.g. Magnifier)

Watch the GIF

See:

Find your apps in App Library on iPhone - Apple Support

Remove apps from iPhone - Apple Support

"Note: When you remove a built-in app from your Home Screen, you also remove any related user data and configuration files. Removing built-in apps from your Home Screen can affect other system functionality"

The referenced article on the consequences of deleting built-in apps is archived and no longer maintained, so it might not fully describe how iOS 16 (the version your tag line says you're running) actually behaves.

Delete built-in Apple apps on your iOS 12, iOS 13, or iPadOS device or Apple Watch - Apple Support

deXvQ6 wrote:

It's not on my phone, just the library. The advice that you can tap or press on the app in Library does not work, of course. It just opens the app. There is also no place in Screen Time to allow or disallow apps from being deleted.

Try deleting it through Settings.

Go to Settings > General > iPhone Storage and click on the app you want to delete in the list. You should see a 'Delete App' option below the details of the app.

deXvQ6 wrote:

I was wrong. The apps are not in my library. They are somehow in the iCloud but not anywhere I can see them to delete.

Are you trying to remove them from the list then? Try opening the App Store, then clicking your profile picture > Purchased > My Purchases and looking for the app(s). If they show a 'cloud' icon, they're not on your phone. They can be removed from this list by swiping right until the 'Hide' option appears.

deXvQ6 wrote:

I was wrong. The apps are not in my library. They are somehow in the iCloud but not anywhere I can see them to delete.

Apps are not stored in iCloud. If you are going to the App Store and seeing a little cloud next to the name of an app, that doesn't mean it's in iCloud. It just means that you can download it again without charge.