Updating to iOS 16.4 from 16.3.x appears to have resolved this issue for me.... or the restart alone had something to do with it since I had just been disabling Siri content search, suggestions, etc. at the top level and at the app level for data heavy apps like Mail, Photos, Maps, all Google apps, etc. I can't believe it's INSTANT again! No lag at all. I've had this issue for months. I recall it starting right after an iOS update. Just to be clear, I have not re-enable content search for any of the apps I disabled. I might try it.