All you have to do to improve on Google at this point is to do less, make it less bad, i.e. a process of removals, not additions. Just do the same thing, but without all the shitty extra stuff. But then what's the business model? (Since that is in fact most of the shitty stuff. Oh sure there's still the SEO spam, and you're in that arms-race, like it or not, even if you're not a
successful search engine, so you do the best you can with that.)
Speaking of doing less, I would love to see the web be more hierarchical or semantic (but not necessarily "the semantic web" as it's currently conceived). Google itself is what made the world reorganize itself. A world where that kind of search exists will reorganize itself around search, maybe not always for the better.
Concrete example of going from a hierarchical/semantic world to a search-based one: Instead of finding your socks in the sock area, which is inside your clothes area, which is inside your "do private things" area, let's say now every sock has a trackable chip in it similar to an AirTag and you just say "Alexa where's the nearest pair of socks?"
Pros:
No effort spent on putting your socks in the sock place. Just throw them anywhere.
Instant access to socks.
Cons:
Big Tech, with all its limitations and machinations, now mediates and controls the relationship between you and your socks.
You succumbed to the temptation to slack off, and now there are socks everywhere. The Roomba doesn't even work right.