Only 60 Hz in Games when screen cloned on capture card

Hello,

at first, sorry for my bad English, because it is not my native language (I’m German), but I will try to explain my problem.
I am relatively new to Linux but I am getting into it. I switched from Garuda Linux to CachyOS a month ago and I am quite happy with it.
I have 2 monitors and 1 capture card (Elgato HD60S+) plugged into my graphics card (RTX 3090). My main monitor is cloned to my capture card, which is connected to my streaming PC. The problem is, my main monitor is a 165 Hz monitor, but the capture card does only support 60 Hz. So far, no problem. It all is fine recognized in the system settings.

But when I play games, the games only recognize 60 Hz. On Garuda Linux, it worked fine, all games worked with 165 Hz.
Is there any way, to solve this and I can get my 165 Hz to work? It would be great, because i switched from Garuda, because it was getting slower and slower with the time (and Steam Vulkan Shader caching took a huge amount of time, CachyOS is a lot faster) and CachyOS is as fast as on day one. But this is for me - as a gamer - a huge problem, which a wasn’t able to fix it by myself. And the easy screen cloning to my capture card is only working on KDE Arch distributions. I tried a couple…
Best regards