What I did was a longer process, but I was determined.
I first downloaded an app called Covenant Eyes*. This is a stand alone browser, so you can still use the internet, there is no private browser, its self-blocking for unwanted content, and it can be monitored by a trusted partner. Then, I disabled Safari and the App Store; this is so your apps cannot open over to Safari (the app, not in app browser) and you cannot download any other browsers or apps**. Then, in Screen Time, block Limit Adult Content and block Google, YouTube, Facebook, Instagram, etc. This will block the entire domain from your browser based on the websites you want blocked.
The whole purpose of this was for example, you go to the YouTube app and go to the privacy policy, then you find a way to get to the actual Google browser. At that point, you would be able to surf the web without any history being recorded.
This has so far blocked any in-app browsers that I have been able to get in.
Please post any questions you have, I would be happy to answer.
* This app will cost $18.99 per month, but has some very good features
** The apps will still update automatically, but I have noticed that it doesn't do it all the time like normal.