Let's say they manage to take just 1% of Google's daily search traffic, which based on a quick Google search (hah) would be about 35 MILLION search queries. If we do a very very rough ballpark estimate of 50 queries per user, per day, it would be about 700,000 unique users... or between 84,000,000 and 168,000,000 USD/year gross revenue.
Now, do I think it's reasonable to expect them to take 1% of Google's search traffic anytime soon? Probably not. I do however think that the sheer size of this market means there is a LOT of missed opportunity by the incumbents in the market that can be leveraged to create niche products that perform successfully by any other market's standards.
So, even if the HN bubble is small there are other bubbles out there. A LOT of other bubbles out there.
Public numbers are a decade old. You're off by an order of magnitude.
The advantage Kagi has over Google is the different business model. Google would never for example introduce a "non-commercial" filter as it would go against their advertising-based business model. Kagi doesn't give a shit about ads and will do whatever that keeps its users paying and so has a non-commercial "lens" (as they call it). I'm not sure how good or accurate it is, but it's at least there which is already more than I can say about Google.
Kagi has a feature to prioritize or exclude some domains. Google doesn't have that despite their size, resources and decades of search experience. That makes it pretty clear to me that Google's weakness has nothing to do with experience or resources and thus a new entrant could potentially compete without either.