How can I get my iPhone 11 photos and messages back?

Before you give up hope, there is a chance your photos and documents were automatically backed up to iCloud. Use a web browser, probably on a computer not your new iPhone unless you are certain you are still using the same Apple ID on the replacement phone. Browse to https://www.icloud.com/ and login with your Apple ID credentials (same as used on your old phone). Look around, there is a real hope at least your photos will be stored there.

It is not up to Apple to back up your phone. If the phone was damaged, it was probably impossible to back up the phone in any case.

Unfortunately, you'll have to manually set up the phone and manually download apps, etc. Photos, messages, etc are gone, I am afraid.