Thanks you for this PR! However, as those that you modified here are module names, I am not sure that they should be modified, at least not like this.

(Also, I think the style guide indicates that "Title Case" should not be used. https://matplotlib.org/stable/devel/documenting_mpl.html#formatting-and-style-conventions Rather "Specialty Plots" should probably be changed to "Specialty plots".)

I do agree with you though that the current approach looks a bit weird. Maybe one should format the modules as "code", so

``pyplot``
=======

etc, but not sure exactly what that would look like.

It is not clear what a "top-level chapter" is in

For everything but top-level chapters

but looking the current documentation it seems like there are no top-level chapters...

I've now changed it to Upper lower.
For most example names in the gallery, there is the Title Case used.

Regarding module names: I think the style guide saies that "`" should not be used.
https://matplotlib.org/stable/devel/documenting_mpl.html#function-arguments

Please don't change the capitalization or remove underscores from module names (you can't import Pyplot or import Axes grid). If you want to make these more homogeneous, I would write e.g. The pyplot module/The axes_grid1 module.

Please don't change the capitalization or remove underscores from module names

My changes are affecting the example gallery, so I thought that the example gallery captions should have names that describe to the users what examples to expect. Are the example gallery captions the right place for module names?
In my opinion no, but I am open to be convinced otherwise.

I think module names should only be used in the reference headings:
https://matplotlib.org/stable/api/toolkits/axes_grid1.html#mpl-toolkits-axes-grid1

you can't import Pyplot or import Axes grid

Yes, but so one can not do import Statistics from the Statistics section

Yes, but so one can not do import Statistics from the Statistics section

Indeed, but pyplot is nothing but a module name, whereas Statistics is obviously a common noun.
Anyways, I've made my point, I don't like the change here but other reviewers can disagree.

Just to confirm that what @anntzer maybe expressed clearer, is exactly what I was trying to say with the example. These are modules and should be spelled as the module, probably with some formatting to make it clear that it is a module.

Thanks for these very quick responses!

probably with some formatting to make it clear that it is a module

For consistency, I've now changed it to The axes_grid1 module , The axisartist module and The pyplot module