This reminds me of the design model of SearX/SearXNG - instead of a distributed forge index, it would distribute the search endpoints of forge instances to facilitate the next steps you outline. It almost feels like a central coordinator or maybe a CDN-like network set of search proxies would be needed to do the actual combining and filtering of results. Maybe it could fit in the Codeberg operational umbrella in some future plan.
In practice Nostr does this step on the client side - one subscribes to relays, then when querying for new content it asks all relays, gets all the duplicate metadata and filters on the client. Huge network use and battery drain on your handheld device, Nostr bouncers have emerged for this exact same reason, a popular software is "Bostr", easy to find examples run by random volunteers but it requires money (disk/cpu/ram): https://bostr.azzamo.net/