Paid plan has been on my mind for a while now.. and as you said, it's complicated. It's in the pipeline.
There's also things like https://coil.com/ who seem like they help support online content creators. I wonder if there's a way to treat search results like "content".
It is possible. I built the search engine [0] that was the first to integrate Coil as a monetization source. It is pretty small, but Coil payments do cover about 2% of the monthly cost to run the service.
Infinity Search also uses Coil. [1]
Here is an article with some thoughts around monetizing a privacy based search engine [2].
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[1] https://webmonetization.org/
[2] https://coil.com/p/runnaroo/Privacy-and-Search-Engine-Moneti...
It would be interesting to sell space against specific queries for a time duration vs per click or per impression.
This approach doesn’t lend itself as much to optimizing for every individual user action, but instead as the quality of the content and users as a whole.
I would focus on a few niches to start which have lots of ad spend that you could get a piece of. Maybe you could then pour those dollars directly into improving the organic results for those niches.