I am using two of the same Dell and model number with OBS Studio on one streaming system and have zero problems. On another system, I have three HP monitors all of the same make and model running OBS Studio without any problems. On another system, I have two Samsung monitors running with OBS Studio with no problems.
There is no reason to keep OBS preview on. You only need to use it when you are testing BEFORE you live stream. When you are satisfied with what you are seeing, disable it. Leaving it on will only suck up more GPU. If you are streaming to YouTube, you leave up a browser window to watch the post process streamed back to you - thats what matters the most.
ideally, it is best to use 3 monitors:
Monitor #1: OBS Studio, OBS stats window, Windows task manager to watch performance
Monitor #2: Chrome browser running YouTube/Twitch to see post process
Monitor #3: If playing and streaming on same box, your game
If you can't afford to buy another monitor, there is nothing anyone can do to help you here. But don't go blaming OBS Studio. For most of us, setups using the same screen device works and works well. If you go put a Michelin snow tire on your Ferrari and a high performance Good Year tire on it as well, you can't go complaining to Ferrari that your car doesn't handle correctly.