I had tried activating the settings in the Apple TV 4K to match the dynamic range and frame rate and it didn't work. I thought let's try that again after the OS update and it seems to be working now.
I get the rainbow bar for a second or two when playing Netflix or Disney+, but after that it runs smoothly until I stop playing (clicking the menu button on the Siri remote) and I get the rainbow bars for a second or two again.
But all in all, it looks like it's working now, I'm still suspicious about the capture card and it's compatibility, but for now as it's working, I'll go ahead and use it and eventually upgrade to a better hdcp2.2 compatible card instead.
Thanks for the help & advices Ambientheater77 & james2brite!
/M