There is a bug which will not allow screen time to work and restrict YouTube. Furthermore you cannot restrict time limit on safari either. YouTube works fine on the safari unless you completely block the website. Will this be fixed?
YouTube Bug iOS 14.6 iPad
This is again, probably something more for YouTube feedback, and not for the developer forums. The developer forums are where developers ask questions to one another, not necessarily give feedback on non apple made apps. I recommend you direct this to YouTube support or go through feedback assistant.