I wish something like the Web Monetization API was a viable path to monetization, but I don't think it is in the current state.
I believe the only current path to monetization that preserves user privacy is context based display ads that work like billboards in the real world. I am working on that now, but the idea is a flat fee to display the ad for N days regardless of views or clicks.
It is certainly challenging, but DDG and Startpage both exist and seem to be profitable.
The key is to monetize and 1.) ensure user privacy, 2.) ensure the monetization method doesn't create perverse incentives in contention of providing better search results for users.