> These days these cards are mostly extinct
Precisely. It's really hard to find a GPU that is passively cooled and typically GPUs have fans that are ultra-noisy when under load.
I had an AMD 3700X CPU (no iGPU on that one) and I really didn't like it.
So one year ago I built myself a little rig: AMD 7700X CPU, Be Quiet! tower, Noctua fan, 32 GB of DDR5 and that series of CPU does have an iGPU. I put it in eco mode (I think at peak it'll draw 95W instead of 105W: no discernible difference which I tested with, for example, compiling the Linux kernel or compiling Emacs) in the UEFI/BIOS and when I use it it's often running in powersaving mode (for example when I switch to a browser, the CPU automatically goes to powersaving mode but if I switch to Emacs or an IDE, it goes to performance mode).
The thing is exceptionally quiet. When it's compiling on all cores I can slightly hear the CPU's fan (a Noctua one) ramping up and that's how I like it: it's very muffled, very subtle, but I can hear it. When I do something else than compiling, it's inaudible.
If you want a really quiet desktop and don't game, a CPU with an iGPU is the way to go IMO.