I successfully managed to use an AMD RX 580 with the Framework 13 i7-1280P using an EXP GDC TH3P4G3 (buy link on egpu.io).
I’m running Pop!_OS 22.04 LTS under Wayland.
In my case, I had to force Wayland to use the eGPU as primary using all-ways-gpu otherwise apps would still start on Intel graphics. Since my setup has 2 monitors (1440p 165 Hz and 1080p 60 Hz) and the dock is meant to be fixed at the desk, I didn’t mind making this switch.
It also seems that for my dock/GPU combo I had to force the GPU to use PCIe 3.0 speeds instead of PCIe 1.1 Don’t ask me why that’s happening, I have no idea. I used the guide from all-ways-gpu here.
Only problem I stumbled upon is that the laptop doesn’t want to go to sleep with the dock connected (even without a GPU inserted in the dock). Made a post about it here.
EDIT: I managed to fix the sleep problem.