I don't know. I turned it off when I first got my 16 Pro.
I initially responded thinking you were complaining about the screen still being on, albeit dimmed, after two hours. I thought that is what you wanted to change.
I have auto-lock set to 30 seconds, but I assume if you set auto-lock to 4 minutes, and with Always On Display disabled, your screen will stay on for about 4 minutes then dim and turn off and the device will lock. My device screen doesn't quite stay on for 30 seconds, but close. Anyway, you can test.
Again, I may not fully understand what you are trying to do. My hope is that I at least help you find what you are looking for.