Currently both FederatedProperties and WikibaseCirrusSearch use the WikibaseRepoEntityTypes hook to alter the entity type definitions.
Specifically they both alter Def::ENTITY_SEARCH_CALLBACK
Given that we have no control over when the extension registration code runs these hooks we can't control which takes precidence.
The proposed solution to this is to no-longer make the changes that federated properties requires as a hook but instead call it after the hook has fired so that it will always be the last thing and therefore take precedence.
This highlights the need to be more careful about our entity type definitions.