For this to work with a desktop PC, you would need to connect your display cable to your iGPU instead of your dGPU. The driver should take care of the rest. This might yield lower performance when using dGPU for processing (probably unnoticeable, depending on circumstances).

I built a new machine pretty recently, also with an RX 7800XT GPU (factory overclocked). When sitting idle at the desktop, the system draws about the same amount of power as my old machine did with an RX 480. So I think trying to put the big GPU to sleep during desktop use might be barking up the wrong tree.

I suggest getting a power monitor, like a Kill-A-Watt, and taking measurements while you experiment. Here are some ideas to consider:

• Are you using multiple monitors? I have read that newer AMD GPUs sometimes draw more power than they should in this case. It might depend on the resolution and/or windowing system in use. (I don’t remember if the reports I read were on Wayland or Xorg.) It almost certainly is a driver issue.
• Are you using nonstandard timings? Have you tried different refresh rates? https://community.amd.com/t5/graphics-cards/which-monitor-timing-parameter-allows-gpu-vram-frequency-to/td-p/318483
• Have you been playing games for hours every day, with no frame rate limit? The graphics card can draw considerably more power pushing polygons at 1440p@180Hz than it does at 90Hz, for example, and I don’t think the wattage progression from idle to full load is linear.
• Are you using recent kernel and firmware versions?

Any halfways decent GPU driver and device firmware will put it into a low power state when it’s idle.

Has the actual KwH increased on your bill? Power bills are like 50% fees so double check the fees aren’t the thing catching you out.