If it's ok, I'd like to keep the shorthands. I had them in the original Page Visibility document and I'm using them in some specs already. I personally find it convenient to conceptually write, for example, "if the document is [=document/visible=]... ", versus, "If the document's [=document/visibility state=] is "visible"...".

However, it it sets bad precedence, I can remove them (or please delete them directly via a suggestion).

Can you give some examples so we can see how widely-used that kind of shortcut is? I couldn't find any myself when quickly poking around.

I think it's slightly suboptimal to talk about a document being hidden instead of talking about its visiblity state, as without following the link one might think it's a general idea of hiddenness instead of the very specific definition given here. But it doesn't matter that much.

A not so great example (I’m the process of rewriting the visibility part to use the visibility change algo, but let’s use it for discussion):
https://www.w3.org/TR/geolocation/#request-position

Any examples that aren't in need of rewriting anyway? :)

No. The other one I thought was using the shorthands was Screen Wake Lock, but turns out it’s using “visibility state”. I’ll remove them as then it’s only Geo, and I’m rewriting it.