(In reply to Dennis Schridde from comment #0)
> During a boot like this, the second card (AMD Radeon RX 560) fails to come up
> and is not available to the system.

That's actually because of:

 [drm:gfx_v8_0_ring_test_ring [amdgpu]] *ERROR* amdgpu: ring 0 test failed
(scratch(0xC040)=0xCAFEDEAD)
 [drm:amdgpu_device_init [amdgpu]] *ERROR* hw_init of IP block <gfx_v8_0>
failed -22
 amdgpu 0000:01:00.0: amdgpu_init failed

the other messages are probably mostly harmless / not directly related to this
problem.

> * Hangs of the entire system when I start Steam using `env DRI_PRIME=1
> steam` (nothing reacts to commands anymore, including mouse clicks, the power
> button and the num-lock key, and the mouse cursor moves very sluggishly)

That's probably related to the above.

> * The firmware and GRUB (and Linux, initially) display at 1024x768, while
> the monitor's native resolution is 2560x1080.

That's a motherboard firmware / video card ROM issue, nothing to do with the
Linux kernel / drivers.