Before I say anything, can you update to newer iOS? I forget which version it was, but one of them around 16.4 or 16.4.1 had an issue that broke Shields where sites only worked if you turned off trackers and adblocking protection. Then in 16.4.1(a) and the newer 16.5 it worked as intended. I don’t know what went screwy with that iOS update, but it was one of the rare times OS messed with things. So I kind of want you to rule that out by updating.
If, for whatever reason, that isn’t what’s happening then I’d have you look to see what Shields settings and content filters you have activated within Brave. You can check that at Settings → Brave Shields & Privacy for your primary settings and then can go one step further to Content Filtering. while there. For example: