CUDA is grayed out for Premiere and Media Encoder, but NOT After Effects.

Premiere Pro, beginning with version 25.2, has depreciated the MPE software-only mode. You can no longer choose software-only rendering in Media Encoder at all, and you can access software-only rendering in Premiere Pro only when you hold down the Shift key while launching Premiere Pro and then checking the box marked "Use software-only rendering" (this is the troubleshooting menu). Otherwise, if that Quadro RTX 4000 is the only GPU installed, Premiere Pro and Media Encoder are both permanently locked to the CUDA GPU-accelerated rendering mode (and Adobe has permanently disabled the OpenCL mode for all Nvidia GPUs for hardware-accelerated  rendering).

By the way, Turing (which your GPU is based on) is now the oldest GPU architecture that is still receiving CUDA updates. Maxwell, Pascal and Volta GPU architectures have their CUDA support frozen to a previous version beginning with the newest branch 570 of the Nvidia drivers. Under that circumstance, I would not be surprised if the next major version of Premiere Pro would require a Turing or newer Nvidia GPU just to even run at all, or else a warning message would pop up singling out unsupported GPU hardware.

That is an ancient GPU by computer standards. I don't know that any Turing era GPUs are still usable in Premiere. @RjL190365 would be the person that knows.