Changing Screentime Passcode

That means that you didn’t enter the Apple ID and password when you set up the screen time passcode. If you did not associate an Apple ID when you first created the passcode the only option is to restore your phone to factory settings and do not restore a backup, as the backup contains the screen time passcode→Restore your iOS device to factory settings - Apple Support

Keep in mind that the primary purpose of a Screen Time passcode is to prevent children from altering settings. That’s why it requires an Apple ID (which can be different from the phone’s Apple ID) and also why it doesn’t use biometric ID or two factor authentication. If it did then it would be easy for kids to bypass it.

An Apple ID is recommended, but not required. And it should not be the same as the Apple ID that the phone is logged in to in the case of a phone used by a minor, where Screen Time serves its intended purpose of parental controls. If you are just using Screen Time to prevent “accidents” by the regular adult user you can turn it on without a passcode.

You don’t need to set it up with a new Apple ID, you can set it up again with the same Apple ID. And if you sync everything on it to iCloud (go to Settings/[your name]/iCloud and turn on all the switches) you can sync everything you previously synced back from iCloud after you set it up as a new phone. You will still have to download your apps from the app store, and your music. But you can’t restore a backup, as that will restore the screen time passcode.

If it was a personal phone and not one used by someone who needed parental controls there was never a reason to have a screen time passcode in the first place.