I tried Kagi and liked the design. Having to log into a search engine to use it is a no-go to me, though. But if there is "demand" for it, I can surely add it. So far, I think I am the only user of Gnod Search.

Neeva does not let me search, no matter what: "We'll get in touch as soon as Neeva is available in your region". Maybe they don't want to deal with users in Europe?

I think for a list of search engines to try, it is best to stick with the open ones. Otherwise, the experience will become cumbersome if every other engine you want to try tells you that you cannot use it for some reason.