The "forgot passcode" isn't working. It acts like I've entered an incorrect passcode.

Try this:

Enter current password when prompted

When it asks for your old password, touch "forgot iPhone password"

On the next screen, select the device you are trying to sign into

Enter your current password

You should be logged into iCloud

Did you read the article at the top left of this thread?

Screen time passcode or passcode to unlock your iPhone?