Related issue in the engine: https://github.com/meilisearch/meilisearch/issues/4932
Request facet distributions and facet stats in your federated search, by using federation.facetsByIndex in the POST POST /multi-search route.
Merge the returned facets in a single facet distribution and stats that is global to the entire request, by using federation.mergeFacets in the POST POST /multi-search route.