I don't really believe anything my phone tells me about what apps are running. I think I'm quiting a music player and the interface disappears, but the music will keep playing. If it's slowing down, closing apps does nothing, but rebooting does.
Yeah, my parents actually close all their apps regularly, whereas I have dozens of apps not doing anything in the background since it doesn't really make a difference.
Tons of FOSS apps doing crucial stuff use tricks, like displaying a permanent notification (which you can then mute) to stay awake.
Also, you need to manually set the battery restriction to "unrestricted" for apps, by pretting on the text in the 2 battery options, and setting it away from "optimized".