Does my MacBook Air M1 support more than one display at a time?

I have an M1 MacBook Air, I connect an adapter to it, and plug HDMI so I can see the screen on a monitor, a bigger screen instead just like my windows laptop, when I head outside, I use it as a laptop, BUT, the problem is, When I connect it to the external display (monitor) it just extends the screen, I tried closing the lid, and it sleeps then, It's literally just an extended display of the Mac, Just like when people connect multiple monitors, I want to see the EXACT screen I see on my MacBook as a laptop, BUT ON AN EXTERNAL DISPLAY (MONITOR)