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?
It's clear you're not an expert, but still somehow here you are telling people to lower their expectations when there is an actual issue.
I've been streaming with nvenc for 7 years and this is not expected behaviour by any means.
I've just built a system and finished two weeks of steady benchmarks, the problem appeared just the other day, and just stole 10-15 fps from most games, but almost 25 frames in some benchmarks.
Consistent 170 no obs, consistent 145 with it just open, 140 with it running.
This is NOT typical.. I've run this same benchmark at 160 fps while streaming like a hundred times in the last two weeks.
OBS is stealing 15 frames that is wasn't stealing just a day ago.
You are in these threads, being entirely unhelpful bro, go outside.
On the bright side, I seemed to have found a fix. For me I actually found it was better when obs wasn't admin, but it was Display Capture that was primarily causing the issues, setting display capture to windows 10 setting made it better, setting it to game capture completely gave me my frames back. Back to 160 + in the benchmark.
There are over a hundred vods on my twitch that prove this is an issue that just started recently and has nothing to do with hardware limitations or expected behavior of OBS.
https://www.twitch.tv/phenohype/videos
Hope that helps