Running Android 14 and somewhat disagree. I have had 1-2 games running in the background after "exiting"/"quitting" the game and dropped from 80-90% battery to 30% in less than 2 hours. (GPS and Bluetooth both disabled). Battery dropped as though I was actively playing with the screen on during that time.

Killing apps has helped me with this issue, in general. However, for the offending game, setting "app battery usage" (specific to Android, not sure of iOS equivalent, if any) has helped better for this issue. Seems a lot of games are trying to load unmecessary stuff and/or sell usage data, despite exiting the game...