Following Kagi's vision of bringing privacy and safety to the web I would promote parental controls inside the browser. Orion would be the first browser to implement this as I am aware.
This may be offered together with a Kagi connection or local.
The parental settings would be locked behind a PIN, 2FAS token or an email verification.
Inside these parental controls settings I would like to subscribe to filter lists and allow or disallow specific pages. Additionally the parent may choose to allow or disallow specific permissions as downloads (applicable to extensions as well), microphone & camera, location and video recording. I could see a feature viable of not being able to access sites without content & tracking prevention as well.
If a children wants to access a specific site they would need to prompt the parent to gain access.
I don't believe in the restriction of access to sites via age verification through external providers, instead I do believe native OS, browser and search engine integration are a promising solution to the problem.