Ok, after all my hours of testing, the only solution is either 1) rolling back to OBS 30.2.3 (this is guaranteed to work or 2) playing Star Citizen in Vulkan.
I don't know why these solutions work. I'm guessing there's a dx11 anti cheat hook that wasn't updated by CIG and that they need to get on it after the release of Star Citizen 4.0. Either way, these are the solutions in the meantime. Goodluck. I hope y'all find this before you waste your time like I did.