How can I delete an app on my iPhone. Now it only allows me to remove it but not delete it.

If you are using Screen Time, go to Settings/Screen Time/Content & Privacy Restrictions/iTunes & App Store Purchases - Change Deleting Apps to Allow.

Then go back and try deleting the app again.

Tap Remove App and a new screen should open asking you if you want to remove it from the home screen or delete it.

Does another menu open? Which app is this?

You may have a restriction turned on under Screen Time, check it.