I can't really see how zero-knowledge proofs could solve this. There is no cryptographic way to prove that software executing on a clients machine triggered a notification. Especially on Linux where an open source notification manager could be modified to reject it.
I'm equally not so convinced on this anonymous ad system they claim to have built. The browser claims to generate an adID based on your history but encrypt this info to the advertiser. Maybe someone who has actually interacted with the ad platform can provide more insight on what information is exposed.
Zero-knowledge advertising sounds practically like an oxymoron to me, but hey they claim to have made it work.
A sufficiently-capable attacker could conceivably trick the browser into thinking a native OS ad-notification was displayed, we do rely on the OS to inform us at this point (though preview versions of Brave do not have this dependency), but we have considered this as well.
The main threat here would be an attacker who attempts to automate the confirmation process, and potentially duplicate it across various VMs or OS instances. Fortunately, we've considered this too. For reasons I hope are obvious, I can't go into greater detail here.
But yes, when you view an ad, that gets recorded somewhere (so that you can get rewards, and the advertiser can be billed).
You decide if you’re comfortable with this or not. The feature is easily turned on or off.