iphone behavior after power off

That is not a list of ‘running’ apps. It’s a list of recently used apps.

They are not running. With the exception of things like navigation, apps generally don’t actually run in the background at all, and if you’ve completely powered off the phone, nothing is “running”.

The recently used list is not automatically cleared when the phone is shut down or restarted.

It has never been automatically cleared, at any time in the 16 1/2 years that iPhones have been around. The only way to clear it is to manually swipe up on each app, but there is no point in doing that because it is just a list, not the actual apps.

There are NO apps in the background, ever. The App Launcher is a list of apps that have run. It is not the apps themselves.

You may have discovered that the iPhone is not really "off" when it is off.