PC SETUP: Ryzen 7 3700x, EVGA RTX 2060 Super SC Ultra Gaming, 32GB 3200 MHz Corsair RAM, 600Mbps down/25Mbps up (wired internet), Omen 27i IPS LED QHD 165Hz 1440p 1ms response.
STREAM SETUP: NVENC(new), 1080P, 60FPS, 6000Kbps, profile - high
PROBLEM: I had the same issue as the original post. Games were running smoothly (Apex Legends, VALORANT, etc.), but streaming software/stream was lagging even though CPU was at 10% usage.
Capping max frame rate in Nvidia settings will work. However, I refused to believe my rtx 2060 super couldn't handle the stream and game at the same time, and I wanted to make use of my upgraded monitor.
SOLUTION: Right-click the streaming app icon (OBS, SLOBS, etc.), click properties, and check the box that says "Run as administrator" under the compatibility tab. This is supposed to move the streaming app to a higher priority, so the GPU will allocate more processing power to the streaming app instead of giving everything to the game.
Depending on the PC setup, there could be lagging at times when there is a lot going on, but the stream should remain stable. I am running max settings with an animated stream overlay and have not had any issues at all while streaming.