I don't know anything about the technical side of this. But I would (possibly naively) think that it would be simpler to have a filter that you could automatically apply to sift bog-standard search engine results for Fediverse instances? Like adding "site:uk" to the end of a normal search, except that your filter term would check a list of Fediverse instances to return the relevant results.
And make it an app/add-on so that people can use it with their usual search strategies.