And yeah - while I didn't have luck with other ideas (e.g. DNS, /etc/hosts ...etc) because of that accounts.youtube.com or say wanting to still allow youtube for the other (toddler which was "home daycaring" because that was closed too) - somehow this Microsoft & Edge thing just works exactly as you would expect it.

And for the occasional "But teacher assigned us to watch this YouTube video" - kid can ask for permission to view particular URL.

That said - at that point we've usually went the route of just opening that particular youtube video on one of parents computers/phones and watching it together (or streaming to living room TV).