This seems very similar to an issue encountered 2 years ago (possibly related to: #94), but clicking "Enable GPU Fan Settings" doesn't stick and the fan speed sliders remain greyed out. Speeds are set to 0 rpm by default.
Dowgrading to 565.57.01 fixes the issue.
It's affecting two different PCs, but both of them have the same setup:
arch kernel: 6.13.2-arch1-1
nvidia: 570.86.16-5
nvidia-utils: 570.86.16-2
card: RTX 4070 Ti