I solved it myself. So NoMachine was actually not able to properly talk to the display adapter.
The solution was to completely disable the VM Display within Proxmox by setting it to “None”.
Additionally, you must either
(1) hook up a physical display to the GPU that is being passed through – even if you exclusively VNC into it
(2) buy a 5€ display dummy adapter for HDMI/DisplayPort and the like. Those things emulate a connected display.
This deactivates the basic Microsoft display adapter.
After I hooked up a display to a GPU output, everything was fine. GPU acceleration and everything is just running as expected now.