Turned off app refresh, apps still refresh

That is not refreshing itself. Your phone has limited RAM (not storage), and iOS manages it be removing app code and data segments of suspended apps from RAM when space is needed by other apps that you have launched. If an app has been removed when you next launch it any transient data is lost, and the app has to start over. Apps SHOULD save their transient data when you exit them (they receive a “signal” that warns them to do this) but not all apps “care” about transient data and don’t do this. So the next time you launch them they must start over. If you intentionally kill apps you can make this problem worse, because killing an app does not give them a chance to save status. Likewise if you force-restart your phone, rather than shutting it down to restart it.

Yes, that’s exactly what I am saying. Never close apps unless they are misbehaving. I’m not making this up. What you are missing is the fact that none of the apps that are listed in the quick launch window are running. All that list saves is the last run status of the apps. They are all suspended, and most aren’t even in RAM except for status stubs. And 3 GB of RAM isn’t that much when iOS is using half of it. My quick launch window currently shows 131 apps. The oldest one there I last used 3 months ago.

Here’s my backup references: Do not close iPhone and iPad "backgro… - Apple Community

No, it couldn’t be Apple. When you say you turned off app refresh, do you mean in Settings/General/Background App Refresh? That will stop apps from starting on their own to do processing, but it does not block apps from responding to Notifications. Apps that have Notifications enabled will run to process the notification, which can involve retrieving new data associated with the notification.