Just remove your headset and it will go to sleep mode after few seconds, or turn the screen off will go to sleep mode.
My Quest Pro sleep since more than one week and QGO is installed. Almost same thing for my Q2. I can't tell you how long a Q3 can stay in sleep mode, I use it everyday.
The QGO app don't use battery by itself.
What drain your battery is Meta background stuff, the auto update Meta feature, the metrics your headset send to Meta etc... You have an option that you can uncheck. This allows you headset to wake up by itself to download game updates or Meta updates or do some Meta stuff.