By default, the Mac will not open a second instance of an App. If you ask it, by almost any normal method to 'open' again it will in fact bring the original open instance to the front rather than launch a second instance of itself.
This, under most circumstances is not an issue. if you need a new window, you can open that too, inside the same instance.
This is a different paradigm to the traditional MS Windows method, where a new window is often a brand new instance of the app itself. This has changed over the years for such as web browsers, where there is now one 'global' app, with a separate process for each tab. This is much more like the Mac has always done it.
So, back to Spaces [or Desktops: Apple seem to use the two interchangeably, which tends to get a bit confusing].
One App wants to be in one Space. This might be considered a failing, but that's how it is.
If you want to use a second Space, then after you open a second window, grab the title bar & use the key-command to change to the Space you want the window to go to. The window will follow you there.
Unfortunately, it is unlikely to remember that if you Quit & relaunch the app - it will put both windows back on the same Space.
However, for multiple apps, multiple Spaces is a great idea. Launch an app, move it to a Space, then right click it in the Dock > Options > This Desktop & it will henceforth always open in that Space.