I don't think that's the best interpretation of complement. Think of complement as "is your users experience benefited by the existence of the other thing". I think that Search qualifies as something that enhances the Facebook users experience (e.g. my cousin mentioned thing that they like doing today, how do I find more about thing?)
Given FBs optimization of the feed for dopamine hits, I don't think search across posts is a high priority (yes, it is table stakes, but whatever they currently use seems to be commoditized enough for their purposes). Group and page recommendations and discovery is another matter, perhaps an LLM may help make that more engaging. It might also be useful for helping users (and brands) moderate their groups and so on. These are also complements, but they aren't external ones.
