while you are in Horizon, or any other places (linux, android, game, etc.), having auto-RCM doesn't have any effect on the battery.
autoRCM is a change and alteration of the boot code to force the console to boot into recovery mode thinking the console is bricked.
If you are in ReCovery Mode (RCM, No video at boot which looks like it's still shutdown, but it's in Recovery), then the program managing the battery's power is not launched yet (it's part of Horizon OS) and therefore doesn't regulate power when not in use. being into RCM (not the same as having AutoRCM!) drain battery all the time instead of making it go to low consumption mode like when the console is in sleep mode.
When you shutdown the console, it doesn't shutdown but reboot.
the boot payload program is responsible for shutting down your console or booting horizon.
(re)Boot > RCM > payload > Shutdown or boot horizon ? -> Horizon -> game/sleep/reboot/reboot to shudown
atmosphere now properly shutdown the console when you choose shutdown and doesn't get stuck into RCM waiting for a payload from your computer/phone/chipset.
If you don't use Atmosphère, run hekate payload again and shoot "shutdown" from its menu.
BUT ATTENTION ! if you plug the USB after shutdown, the console will automatically boot again, and you'll be back into (invisible) RCM, draining your battery if you don't keep it powered.
if you want to charge your console while it's shutdown without going into RCM, plug it to the dock BEFORE shutting down.