AFAIK your drivers support PRIME and your system is configured to use Intel for rendering desktop which is one part of a PRIME setup. prime-run is just a script, you can download (not install) nvidia-prime and put the script in it to /usr/bin.
OpenGL games will need prime-run, Vulkan games and DXVK games running via VKD3D or DXVK should pick up the Nvidia GPU automatically. The graphics switching in Nvidia control panel is for switching the entire session, this isn’t obligatory for running games via PRIME.
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