For android notification will appear on tray at the top and trigger method of onBackgroundMessage (when app in background or terminated) ONLY. You have to use third party solution like flutter_local_notifications or overlay_support to display notification during onMessage (app in foreground).

For iOS, when notification is clicked (when app on background, terminated or foreground), method onMessageOpenedApp will be triggered. For Android, this scenario will work when app on background or terminated only (if head-up notification display/banner is enabled - you need to create channel_id for android)

You no longer need to send click_action: FLUTTER_CLICK_ACTION on data payload in order to have clickable event on notification. FirebaseMessaging will handle for you