I don't know about nonprofit. The only open source effort at web indexing and searching that I know of is YaCy. I'm not impressed with it, but it was a technically ambitious project, but now seems to be stuck at a 2009 level of technology. Being written in Java also doesn't help endear it to me.

I've come to think of web search with integrity as a probably unsolvable problem. Maybe a heavily publicly funded public option could put a dent in the problem, but of course the current climate has turned me against even the public sector.

Decentralization of a spidering operation or a database operation, I would think, would make it impossible to deliver a search result promptly. Best I think can be accomplished with a decentralized or defederated effort among noncommercial participants would be offering the end user search agents rather than instant search results. A search request would propagate throughout the network of (I would think) shards of database over the next few minutes, and search results would come back to the initiator (by email perhaps) over the next few days, with a few stragglers over the next few months or even years, with cancellations of search request probably also taking some time to propagate.