Forgot screen time password.

You've only three choices:

1. Restore data from a backup (if you have a recent one) created BEFORE you set up that passcode
2. Cohabit with the restrictions you set up
3. Erase your iphone and start from scratch. Creating a backup in your situation doesn't help, since that passcode comes back again during a restore procedure.

Regards

Giulio

Clarifying my original post, ProustGiulio, the context for my comment was about backups. iOS 13 does not include the screen time passcode in the backup any longer. It used to be that for iOS 12 you could just read the screen time passcode from a backup using a tool. It's stored on the device and in iCloud. Simply restoring a backup will not change the screen time passcode without fully wiping it using the "Restore iPhone" feature.

I thought that the latest iOS no longer includes the screentime passcode

I don't know who gave you this info, but on my XR running iOS 13.3 the ScreenTime passcode is still there (if you enabled it).

Regards

Giulio

I have successfully removed the screen time password from an iPhone running iOS 13.

1) Connect iPhone to a Mac

2) Make a local backup of the phone

3) Use "Restore iPhone", which effectively reinstalls the OS from scratch, and restores a backup. Note, this is NOT the same thing as "Restore Backup...", which only wipes and recreates the user data and does not reinstall to OS. For iOS 13, the screen time pass code IS NOT INCLUDED in the backup.

Once your phone is restored, you will be able to configure a new screen time passcode, and re-enable share across devices without this passcode being overwritten. (however, as an aside, there appears to be a different bug in which devices aren't getting the new screen time passcode, I'm working with Apple Support on this currently).