also add missing final dots in the sentences below? (throughout the docstrings you edited here)

Trying to not get carried away too far. Otherwise the PR gets endless and even more terrible to review. These sentences need rephrasing anyway. It's better to leave them alone for now and do everything in one go when I come back.

Is chaining or like this the style we want? Could do as str, path-like, or file-like which reads better to me....

That's how the numpydoc docstring guide describes it:

shape : int or tuple of int

Currently we use a comma for simple tuples, e.g. center : float, float.

I don't have a strong opinion on this, but if we change that, we need another convention for tuple to avoid ambiguity (could be (float, float)). Everything should be changed consistently throughout the docs and we should document it in "writing documentation".

If you use the Oxford comma it’s not ambiguous:

A, B, or c

A, B or c

Though I would tend to enclose tuples in brackets just to be clear

Why has bytestring been dropped here?

Because it's a path-like?

I was adding path-like, because that's clearly missing and relevant. Technically, that would be enough (str and bytestring are path-like). However, that's not quite helpful. I don't expect all of our users to know what a path-like is, less that a str is a path-like. The newbie can now still see that a string is fine, and that's the most basic use-case. OTOH, a bytestring is already a bit more advanced. Users who know bytestrings probably know path-likes (or at least could guess that if str works, bytestring will likely too. So bytestring is not giving as much additional information that it's worth explicitly mentioning.