Tying the grounds of multiple devices together over USB cables is likely to create a ground loop. Grounding is supposed to be a tree, rooted at the stake in the ground out by the electric meter. If you don't have that, every loop becomes an antenna. That's why braids are usually grounded only at one end.

This matters when you have something as RF noisy as a plasma cutter nearby.

If you have a scope, you can start looking at signals to see where there's RF hash. Then you can try putting ferrite inductors around various power and data cables to see if it helps. Often it does.

There are USB opto isolator cables.

I'd really like to see a big red switch on that setup to turn everything off. If somebody like a first responder ever needs to shut that thing off, it's not at all obvious which plug to pull first.

(I used to use the rather antiquated plasma cutter at the original TechShop. It never started properly. Plasma cutters start by creating an arc between electrode and the nearby nozzle. That makes some plasma, which is then blown out to the workpiece. Once there's plasma from electrode to workpiece, the nozzle is cut out of circuit. The one at TechShop had a consumable copper electrode and a consumable copper nozzle cap. The electrode is supposed to get all the wear, because the nozzle cap is only involved when the arc starts. TechShop's machine often failed to cut the nozzle cap out of circuit, and it consumed nozzle caps faster than electrodes. TechShop sold nozzle caps.)

FWIW (and I know I didn't mention this) the cable I was originally using for the 6040 CNC router is a "double shielded" one which I bought in the past specifically for EMI reasons, but it wasn't immune to the pilot arc ignition.

I haven't tested it to see how good the shielding is but I haven't had any EMI-related disconnections since switching to that cable. (Other than the plasma cutter ones).