I'm not an OBS expert, so don't take this response as being authoritative.
But hopefully you realize that doing window or screen capture, rendering to the OBS screen, possibly twice if using Studio mode, then encoding for streaming is REALLY demanding on a computer. Make that SUPER demanding Granted you have a upper-end GPU, but there are still internal memory transfer and other I/O constraints, and you are re-scaling on top of things. Seeing your are at Win10 v2004 not sure the differing monitor refresh rates issue applies to your situation.. I think not, but...
Anyways, you post doesn't summarize what you've already tried so not sure how much of the following is obvious, or??
How busy is the CPU, GPU, RAM, disk, network and other I/O when gaming and OBS not running? How many plug-ins are you running in OBS? How optimized is your OBS setup? ie- do you have enough headroom to be running OBS?
For testing purposes, Have you tried keeping Base and output resolution the same (= the monitor you are capturing), and rescaling on Stream output?