OBS is doing what you have asked it to do - record the screen with OBS on it
So, your options are
- put OBS on another monitor
- minimize OBS so not visible (yes, that then creates its own issues on how to control OBS, which is where StreamDeck and other such solutions come into play)
- don't capture the display, but only the desired Window (App) that you want
I'm not aware of a way to capture an entire display/monitor, except a single app (OBS, in this case)
