Screen time passcode
So I’m reading that to bypass the screen time passcode you have to factory reset your iPhone but you can’t factory reset the iPhone without that passcode?
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I don’t know where you are reading that, but it’s not true.
Follow the instructions in this Apple support article—>If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support
After restoring to factory settings (which is what the above instructions do) you cannot restore your backup, because the screen time passcode is restored as part of the backup.