Copper being a relatively 'soft' element is limited to how small a wire can be drawn out to, 56 AWG is approaching the physical limit of drawing it out. However, the 1 Megohm resistor mentioned was not made with cooper wire, at the very least it was Manganin and more likely an Evanohm alloy. Evanohm has been drawn down to as small as 0,000,4" (0,010,16mm) for many years, I have wound resistors with 0,000,7" (0,017,78mm) wire and it is not easy. The wire will break at the slightest jolt to it and it is a lot tougher than copper or copper alloy. Yes the wire is difficult to 'see', the lighting must be aimed exactly in order to 'see' the wire, preferably with a darker background for contrast. There has been several manufacturers in the US over the years that made this fine wire, no need for the Swiss' fine capabilities though.
Depending on the size of the bobbin, the 1 Meg resistor was wound with wire <0,000,9" and some of the smaller ones used 0,000,4" wire. Note that the wire sizes quoted here are the actual diameter of the resistance wire and not the finished size with enamel coating on it.
I do not know all of the finer details of making very fine wire but diamond dies are used with progressively smaller holes in them. As a nod to the difficulty of drawing out these fine wires, the last quote I got on 0,000,7" Evanohm wire was $18,000/pound and that was a few years back!