My ThinkPad X1 Yoga is on Kubuntu 21.10, and I found this Razer eGPU enclosure on Amazon:
Razer Core X Aluminum External GPU Enclosure (eGPU): Compatible w/ Windows & MacOS Thunderbolt 3 Laptops, NVIDIA /AMD PCIe Support, 650W PSU, Black
I know that people have been using it on Linux for many years now. I want to say at least since 2017 or 2018, but I am not 100% sure. I am guessing support for it is better today than it has been. I would think the desktop environment is immaterial as to the support, at this point.
I don’t get the need for an eGPU except in the most extreme cases. You are basically cutting performance in half because of bandwidth. eGPU’s top at x4 PCIe Gen3