The Framework Desktop motherboard does actually have a PCIe x4 slot, their case just doesn't expose it for whatever reason. But you can buy the board separately and put it in your own choice of Mini-ITX case which does.
First I've heard of this thread (I haven't spent much time on the forums for a while), but my Framework Desktop definitely has the PSU noise issue, and it doesn't seem correlated to system load. Otherwise a really solid machine.
That PCI slot has low power output, not suitable for what people would plug into it. Easier to cover it than run into support problems. It won't run a GPU directly. It will run an Oculink card which will allow use of an egpu.
I can't imagine why you'd want to buy a beefy SOC with unified memory, only to have it host a discrete GPU through it's narrow PCIe x4 interface. You'd be better off with a traditional CPU that supports a proper x16 slot.
[1] https://community.frame.work/t/noisy-psu-fan/74751