You're running into rendering lag, which is caused by OBS not being allowed the necessary GPU resources.
There are 2 options
- lower your in-game settings so that you're not fully using your GPU (limit framerate, reduce settings)
- try the new 24.0.3 feature -- turn Game Mode on in windows settings, and run OBS as administrator. This is supposed to tell windows to allow OBS the necessary GPU priority, allowing it to perform the necessary rendering and encoding.