Most Linux distros allow a great degree of granular control over who can do what when using the operating system, and pureos isn’t one of the exceptions. The issue is you have to set up a user for your teenager and manually assign that user to groups and grant and revoke permissions.
None of this is very convenient on the phone at the moment. There are plans to add the option to log in as some other user via GUI to Phosh, but that’s a ways off.
A “simple” thing to do that would give you a lot of control would be to set a root password and remove the default user from the sudoers file, although that is more comlicated in pureos than in other distros.
And I was sort of under the impression that while Phosh uses GTK, it’s not really based on any existing DEs. Of course, that application could probably be used in PureOS and other distros anyway.