If a card "becomes" something else (such as through the use of Skilled Animator, turning that card into a 5/5 artifact creature), and you later use an ability that creates a copy of the affected card, would the copy also be a 5/5 artifact creature or would the copy rely on the printed text of the card being copied?
No, you won’t copy those changes.
When you create a copy of something, with say Sculpting Steel, the original object is copied as printed (or as created if it’s a token). The only exception to this is that you copy any other copy effects that already apply to the thing your copying.
For example, if you copy Juggernaut with Sculpting Steel, then the original Juggernaut dies, and you then cast another Sculpting Steel, it’ll become a copy of Juggernaut when it copies the first Sculpting Steel.