Simplest implementation is that an instance searches its own content while sending requests to federated instances and merging their results in with its own based on whatever method the instance admins want (whether it puts its own results at the top, or treats them as one set, or whatever). That could cause a lot of traffic and has a load of latency while your search spreads out hop by hop, to the instances that yours is federated with, to the ones they're federated with, etc. Plus you'd need a mechanism to stop instances from sending a search to an instance that's already got it, to avoid hammering instances that have multiple federation paths to yours. Not an easy problem.

You might be able to do some kind of index publication where an instance publishes the most notable posts for other instances to include in their indexes, so that when you search it could show you results from among hot posts elsewhere in the fediverse - not an exhaustive list, but a search within posts that are getting attention.

There's also other stuff I'd be tempted to experiment with, like using some kind of TF-IDF ranking to choose what counts as "most notable", rather than just activity or view count, so that posts that are particularly relevant to certain topics could be publicised. An instance could even choose to filter that, so for example an instance who chooses to focus on tech topics could publicise highly-relevant tech posts but filter out politics keywords even when a post gets high relevance scores, so that political discussion on that instance is less visible, even when searched for.