Do any of your underperforming games have a screen that shows which GPU they are using?

I haven't found any that do but I can try launching a few and searching.

Take a look in each game's graphics settings. Not all of them show it, but some do. In Baldur's Gate 3, it's shown in Options: Video: General: Display Adapter. In Elite Dangerous, it's in Options: Graphics: Display: Adapter. There are other ways of trying to determine which GPU is likely to be used by default, but seeing it directly in-game is the best way to be sure.

Does an overlay appear in the top left of the screen if you put DXVK_HUD=devinfo %command% in an underperforming game’s Steam Launch Options?

For the 3 I've checked so far no, I don't see that.

The fact that you see no DXVK overlay when using that launch option suggests that either none of the games you tried use DirectX 9/10/11, or there's something missing/misconfigured/old in your Vulkan driver stack. I would expect System76 to be able to help with this more efficiently than we can, since they sold you the system for use with Linux and are known for being competent.

EDIT: I just noticed your other comment that shows Pop!_OS 22.04 LTS as your Linux distro. That release predates your GPU model by about a year, I think. It seems likely that you just need to get a newer kernel, firmware, and graphics drivers installed. This stuff is available upstream of your distro, so it shouldn't be too hard for someone who knows Pop!_OS well, like System76. :)