I don't know if you have found a good filter service already or if you bought a kosher phone but check out microsoft family safety, I think it'll help you tremendously. It's free and works on android and computers that run windows and it also offers a lot of really good accountability features and a really good filter system. You can block the browser entirely as you said you wanted to and you can do it to other apps as well and if you want, the family organizer can also set time limits on the device entirely and on specific apps too. They also have an allowed websites only function (you can also block specific websites) and I can drop down my list of allowed websites which include many secular websites you may need like fedex or google drive so you don't feel trapped or anything. All your website activity is also available for your family organizer to see but it's different from most other accountability programs because they don't simply report the general websites addresses you visit, they take it a step further and they archive all the pages you opened on the website with their unique links. So this gives your family organizer the ability to see the specific pages you opened on a given website and he/she can open those links to see exactly the pages you opened and exactly what you saw. The family organizer can also see all searches you made and microsoft family safety has a good A.I. in order to report some risky searches that you may have made and this is all available for your family organizer to see on the app or on the website. All non risky searches are all also archived and available for your family organizer to see right underneath those that get flagged as risky. All this is available for your family organizer to see through the microsoft family safety apps (on android and ios) or through the website and the organizer will get weekly emails with all this data.
So given all this if you get microsoft family safety you wouldn't even be tempted to search up p websites or anything similar in the first place if you set someone appropriate as the family organizer. By the way they also have an ios and android app so all that data is available for the family organizer to see anywhere and they can edit the settings or allow any websites that you need that get blocked (if you're using the allowed websites only function) on the go and from anywhere. It works fine with webchaver also and if you have a computer that runs on windows you can add that device along with your phone to have the features apply on both devices. I have it on computer and on computer it blocks all other browsers (but you will have to download microsoft edge, a normal browser like google chrome) and it should do the same on android also.
I hope this helps with the access you may have to unfiltered internet. The filters are also optional but the accountability features are not and they are turned on by default so neither you nor the family organizer can turn it off. Post below if you end up getting it because there are a few websites that will be allowed even when you use the allowed websites only function. Those websites are only microsoft websites but you have to block 2 of them specifically the xbox website and also this website:
account.microsoft.com/family That's only because microsoft family allows you to leave the family group if you're above 18 but you can only leave with those 2 websites. So once you specifically block them you will be good to go.