iOS does support a form a call screening, called live voicemail, which transcribes the message being recorded by the caller and lets you pick up the call if you want. iOS also supports ambient song identification, with history, which I use frequently. Safari supports extensions, and I believe other browsers can as well, but can't speak to that as I really only use Safari in my phone, even though it's not my primary browser on desktop.

Figured I'd drop a comment to let you know about the others though!