My hope is for something like YaCy with a web-of-trust overlay. I'd want it to only show results from peers that I trust, and if garbage starts showing up in my search results, I want to know from which peer it came so I can un-trust it.

Which in my mind is somewhat of a middle ground between a search engine and a directory: what I'd want is a whitelist of curated directories that contain domains to be crawled by my search engine.

You'll probably enjoy Curlie (created by the former DMOZ maintainers) and Neocities (try out different tags for better results)

https://curlie.org/en

https://neocities.org/browse?sort_by=last_updated