How to prevent Kids getting access to the Internet from 3rd party App on iPhone

I have screen time enabled on my son's iPhone. In the content settings I have Safari turned off. I have the installing apps turned off. I have the the listed websites to "allowed only". However, my son was able to access the internet through a third party app. It is a fitness app but it had a shopping section and by clicking the shopping area he could access the internet and thus any site he wanted to and bypassed all the settings I had in place. I know how he is doing it but shouldn't there be some way to prevent this from happening. I know how to put time limits in place for the app and I can see the websites visited and can block each one. I will probably just delete the fitness app but it is unnerving that many apps have a back door access to the internet. Does anyone have any insight in how to prevent this?

[Re-Titled by Moderator]