Apps stay in background even after turning the phone off
That is the default behavior of Android from Lollipop onwards. See this blog which talks of that ( Recents (or Overview)). It is only a list of apps that you used is shown and it doesn't mean that these are running after reboot, so it shouldn't be a concern (unless you want to hide some app or web page that you visited). You can check running apps from settings and you would see that these are fewer than what you see in the overview

Only on earlier versions they would be cleared on reboot