I've been considering dabbling with something like this to connect up with my Lenovo Legion Go but the prices aren't exactly keen for what it is :s
I've been spending a lot of time at my daughters flat recently so I was looking for something to help me play a few games on my really quite old laptop, a Thinkpad T480 (i5 8250 CPU). I saw a Razer Core X Chroma on auction with no bidders so I put the minimum bid in a few seconds before the end and won it. I happen to still have an old AMD Vega 64 which I never got around to selling. So this was a fairly low cost way of trying it and I can probably sell it for the same money I got it for if I decide it's not for me. It also acts as a docking station with USB ports and an ethernet port on the back.
Well it does allow me to play a few games. The most demanding one I play is Quake Champions so not exactly cutting edge. If I put most of the settings on low it can hit over 100 fps on an external monitor and 70 to 80 fps on the internal monitor. But it still feels glitchy for some reason. Putting vsync on and restricting it to the 60hz of the monitor helps a bit. It's certainly playable now although it still feels weird. That may be because of the small 14" low refresh screen, playing on the laptop keyboard and a different mouse that has a completely different sensitivity. I think the old CPU is probably holding it back the most and if I recall this laptop didn't have all Thunderbolt lanes enabled. I guess it's to be expected that it will feel different to a desktop gaming PC with a widescreen 34" high refresh monitor. But it is playable and I expect single player games will be great with it. I may also upgrade the laptop at some point soon anyway. I've never had an eGPU before so it's another toy to play with for a while.
For the Legion Go you can get portable eGPU's now (take a look at the GPD G1 eGPU) although it will indeed be a slightly costly solution.