The one thing I'm aware of is Brave's Goggles project: https://search.brave.com/help/goggles - it basically allows you to set up your own ranking algorithm with a specific syntax (it links to Github repo and, there, to a white paper).

I haven't seen more attempts at similar things, which doesn't mean they don't exist though. (There were mentions of a similar feature being added when Elon Musk was about to buy Twitter, but just gossips)