Not sure what to troubleshoot with AdGuard, but from consulting mine that's working well, I'd ensure that both "Safari protection" and "Advanced protection" are enabled in its app, and that all of its Safari extensions in the system Settings app are enabled (and the main one is set to "All Websites: Allow").

Ah thanks! I only have Safari protection enabled, the advanced one requires me to pay (though I don't remember that from when I installed it a couple of months ago).

Saw someone else in this thread mention the Orion browser - I will give that a try for now. If I'm not satisfied I'll try paying for AdGuard. Thanks for the reply though!