Why does the 3DS talk about Sleep Mode when you press the Power Button?
Solution 1:
It's just poor copywriting. Closing the 3DS in a game includes all the features listed except that street pass is not enabled when in a DS game (3DS games still allow streetpass when sleeping), so you certainly don't have to enter the home screen just to put it to sleep.
That screen itself is just a tutorial to teach you that you don't have to press the button to do that; you just close the device. You can close the device on the home screen (not the power button screen) and streetpass remains active.