"This article indicates that you can do this by selecting the sketch in the browser and timeline and then doing the copy. However, this does not work for me, see the attached screencast"
See my earlier comments. You can copy the sketch object itself, in a Direct Modeling design, just not in a parametric design. So, the article is not incorrect, it is just missing that information.
"But what is the difference between copying a sketch and copying all its elements in terms of what is put on the clipboard?"
The main difference is the number of entities on the clipboard. If you copied a sketch (again, only in a Direct Modeling design), there would be one entity on the clipboard - the sketch. The sketch contains all its entities, but is still one item. The difference is like carrying a shopping bag full of groceries vs carrying all the groceries individually in your arms.
"the issue is that there is a mismatch between what the document says should happen and what does happen."
Yes and no. Agreed that the article should contain the information that this is only for a Direct Modeling design
"The fact that copy is greyed out in the context menu, whilst ctrl+C still works, must surely be a bug."
I might have missed it, but I did not see any cases in your video where Copy was grayed out in the context menu, but CTRL-C worked. I have not seen any such cases myself, but if they exist, then yes, that would be a bug.
One other comment. There were a few cases where even CTRL-C did not work in your video. This is explainable, if, admittedly, confusing. A "profile" object (the shaded area created by closed curves) is not copy/paste-able. It is not a sketch entity itself. It is considered "derived" data, not "primary" data. Arguable, certainly, but that's the way it is.
Jeff Strater
Engineering Director