I’m a little confused. Do you NEED to use Stage Manager to connect to an external display and have a full screen app on an external monitor?
or will my 2018 iPad Pro (not SM compatible) still be able to connect to an external display and have a full screen app (not screen mirroring) on the external monitor?
Your iPad will only be able to mirror unless you're using an app like a video player that utilizes the full screen.