So I really dig the vibe and character design changes that have gone on throughout the years (tachikoma, major, etc.) and they can easily explain it by saying the Major had work done over the years to look different as time went on...
What I never got was how in the original movie, she had to be nude to cloak (if I recall correctly) but in all the prequels (ARISE, Laughing Man, etc.) they can cloak with their clothes on.
No you didn't recall correctly. She was never nude, she was always wearing a skintight suit. Did you not see her nipples in the Intro (where she was built together)? So she obviously has nipples an a fully functionable vagina (minus childbearing abilities). In case you wonder, the manga goes into more details about her private live and private parts. The english version from Dark Horse is censored, 3 pages are missing.
When she jumps from the rooftop at the beginning, no nipples to see, just a small bulge so they are obviously behind something....
Also when they hunt that brainhacked guy over the market, he is also wearing a cloak device which is literally a cloak. Kusanagi cannot cloak unless she has skintight suit on, thats why she is always dropping the cloth above it.
These cloaks are made of some kind of fabric material so you can wear them, but Bots like Tachikomas can have a similar material on their hull so they can cloak too.
Kusanagi has a strange relationship to her prosthetic body often running around in fetish styled cloth, she also said she wears sexy outfits to distract males. As a male myself i found her outfits anything inbetween embarrasing and hilarious, but i dig her "attention warfare" style.