My GPU (RX 5600 XT) does not appear as an option in this menu:
My card does meet those requirements and I have Radeon™ Software for Linux® installer version 22.20 for Ubuntu 20.04.5 HWE
installed. I have a similar issue with DaVinci Resolve.
The interesting thing is that when I run blender as root, Both my GPU and CPU appear as options.
Here is some information I get from lspci -vnn
Subsystem: XFX Pine Group Inc. Navi 10 [Radeon RX 5600 OEM/5600 XT / 5700/5700 XT] [1682:5710]
Flags: bus master, fast devsel, latency 0, IRQ 77
Memory at d0000000 (64-bit, prefetchable) [size=256M]
Memory at e0000000 (64-bit, prefetchable) [size=2M]
I/O ports at f000 [size=256]
Memory at fcd00000 (32-bit, non-prefetchable) [size=512K]
Expansion ROM at fcd80000 [disabled] [size=128K]
Capabilities: <access denied>
Kernel driver in use: amdgpu
Kernel modules: amdgpu```