With a Dual Monitor setup, does one Application stay on the extended screen?

I am looking at the options of a Dual Monitor setup, instead of a Curved one.

Right now I am on a single 24" monitor.

I've seen videos of pros and cons of both.

One thing that springs to mind, specially on a Mac Mini, is if you move your Email over to the Extended Screen for example, or a Safari Tab with say, a Streaming Video running.

If on the other screen you switch between Music, or Photoshop - does the Extended screen's "occupants" remain there? Or if it is it like on a Curved Screen, where if you switch to another App, the one up on the right just goes to the Stage Manager?

My aim is to have the means of "sticking" one app on that Extended screen (be that Mail or even a website page I am testing), but that it doesn't disappear off to the Stage Manager when I do something else. Ie right now on my browser I am trying this. If I click Teams, up comes that, and "this" window disappears.

What happens to the windows on the RIGHT Extended screen.

Thanks.