FWIW new laptops are surprisingly cheap. E.g. this (albeit not new) only cost $400 https://slickdeals.net/f/16843367-asus-zenbook-open-box-excellent-14-5-2-8k-oled-120hz-touch-i5-13500h-8gb-ram-399-free-shipping
I see your xps 13 9310 has a 11th gen Intel CPU. It would be a bit hard to find cheap second-hand mini PCs from reputable brands with 11th+ CPUs. But you can find many mini PCs from some Chinese brands (Minisforum etc).
Another option is frame.work main board + a case https://www.theverge.com/2023/3/23/23652939/framework-cooler-master-sff-pc-case but I think their parts are overpriced if you don't value repairability etc.
Oh wow, I didn't know SFF machines have the space and the port to use a dGPU. That opens a lot of doors to me.