Their Add button becomes Request; you approve or decline.
In Broadcast: Server, People, Requests and reports; requests wait under Server, Activity.
In Classic or Neu: Settings, Account & Access, Requests and reports; requests wait under Activity.
On a child’s account (a Basic user), switch off Add titles themselves. Their Add button then says Request: what they pick is kept exactly as they chose it, and they’re told it went to you. Set it when you add the account, or with Edit on it later.
Requests wait here.
Approve adds the title for them, as they asked, and the library says who asked. Decline can carry a note they’ll see. The number on the tab is how many are waiting.
A notice on your phone for each new request: tick Requests on a notification under Server, People, Notifications (Settings, Notifications in Classic or Neu). Get notices on your phone, in Show me how, sets that up.
The family filter on Discover keeps their rows to their age, too.