Not any more "sentient" than existing LLMs even in the limited chat context span are already.

Naturally, »nothing new of interest for you« here is indeed just a proxy for »does not involve any significant concept that you haven't previously expressed knowledge about« (or how to put it), what seems pretty doable, provided that contract of "expressing knowledge about something" had been made beforehand.

Let's say that all pages you have ever bookmarked you have really grokked (yes, a stretch, no "read it later" here) - then your personal model would be able to (again, figuratively) "make qualified guess" about your knowledge. Or some kind of tag that you could add to any browsing history entry, or fragment, indicating "I understand this". Or set the agent up to quiz you when leaving a page (that would be brutal). Or … I think you got the gist now.