Final answer:
To address a forgotten Screen Time passcode, update your device's software, perform a reset as a last resort, and if needed, seek help by contacting Apple Support or visiting an Apple Store.
Step-by-step explanation:
If you've forgotten your Screen Time passcode and can't use the 'Forgot Passcode' option or sign out of your Apple account, you still have a few steps you can take. First, check if there's a recent software update that you can install, as this could potentially fix the issue.
Should updating not be an option or does not resolve the issue, then you may need to consider a reset. You can reset your device to factory settings, which will erase all your data, but should remove the Screen Time passcode as well. Before you resort to this, make sure to back up your data.
If these steps seem daunting or if you're not comfortable performing a reset, the best course of action would be to either contact Apple Support for guidance or visit an Apple Store for assistance. They can provide you with the help you need to recover your device without losing your data.