Yes, the brake master cylinder is also used on the Giulietta.
The brass sleeve is best explained by taking a small detour: Brake fluid attracts moisture. The moisture condensates and, because it is heavier than brake fluid, typically accumulates at the lowest points in the brake system (e.g. at the bottom of master and slave cylinders) where it starts to corrode and pit the bodies, which eventually leads to leaking cylinders that cannot be fixed by using a new kit. At that point, there are two options: (1) replace the cylinder or (2) drill it out and use an insert that provides a clean and unpitted surface for the pistons and seals. For the 2nd option, brass which is machined and inserted as a sleeve. You'll need to ask around who could do this for you.
BTW, I was told "spun" brass with metallurgical grain that is circular (and therefore perpendicular to the piston action) is better than extruded brass with longitudinal grain -- however, this difference is probably less important than having proper, circular dimensions and roundness.
When I rebuilt my brake master cylinder several years ago, I spoke in great detail to the folks at White Post (Billy) and Karps. White Post uses brass sleeves and Karps uses stainless steel. Please read through my article and speak with the folks at both places before deciding what to do. At the time I was not made aware of spun brass. So, I know nothing about it. Brass is soft and does not hone or hone as well as a harder compound. The cross hatch pattern left by the honing process is essential to a quality rebuild and years of reliable serve. Brass is more corrosive and softer than stainless. Since brass is much softer than the pistons, there is a tendency for irregular wear in the cylinder in the form of chatter marks. This can lead to a premature failure.
I have a NOS original Girling brake MC in stock at £175. We can also re-sleeve in Stainless for £140, although as your are in NJ it may be cheaper to find one locally as you need to send us yours first.
Great write-up, ossodiseppia! I also prefer stainless over brass but I did not have that option available when I did my brake calipers (and it's probably more difficult to find a shop who can handle it).