Add search api integration test

Postponed for 📌 Add AI Search basic functional test coverage Active depending on what that ends up covering.

@scott_euser - are you going to implement or should I assign this to me and ask for PR when tode?

I think it can be closed actually as I added functional test coverage which covers integration with search API in 📌 Add AI Search basic functional test coverage Active already.

I haven't extended that yet to cover the Boost plugin yet for database. For SOLR it's probably not possible to cover.