Three other thoughts:

1. There are a lot of boxplot examples
2. bxp and boxplot never have their difference coherently explained as far as I can tell
3. Are PRs like this one desireable? Better linking in the docs seems like a positive, but I don't want to add uncesssary noise

This is very welcome. We just haven't gotten around to doing every example yet and have been counting on people just adding them as needed.

I didn't add every function used in the examples, rather I erred on the side of caution against overlinking things such as set_ylabel and tried to include only the functions that the examples focus on.

👍

1. There are a lot of boxplot examples

There's quite some redundancy in some areas of the examples; I guess for historic reasons. More and more examples were added and it was not always checked if this adds something new or if there should have been some rearrangement. A bit consolidation would be good. But that's also a tedious process. One has to find out what the core message of each example is and if that's already explained in another example. If you see something that is duplicate or if some examples could be merged easily, you're welcome to open a PR.

3. Are PRs like this one desireable? Better linking in the docs seems like a positive, but I don't want to add uncesssary noise

Yes definitively. The references are value in particular because of the backlinks from the functions to the examples. But choosing the relevant references must be done manually.

Generally, we add the corresponding pyplot functions as well, even if they are not used

Ideally this could be automated to catch both pyplot -> axes and axes -> pyplot?

Generally, we add the corresponding pyplot functions as well

Done

Generally, we add the corresponding pyplot functions as well, even if they are not used

Ideally this could be automated to catch both pyplot -> axes and axes -> pyplot?

Unfortunately this is all very manual: We're tuning our content so that sphinx-gallery does "the right thing". But sphinx-gallery does not know anything about pyplot <-> axes relations. And we cannot easily patch this in.

Probably the most promising direction of automation would be to customize the generation of the pyplot ReST code, so that it references the respective Axes minigallery; i.e.

matplotlib.pyplot.boxplot
=========================

.. currentmodule:: matplotlib.pyplot

.. autofunction:: boxplot

.. minigallery:: matplotlib.axes.Axes.boxplot
   :add-heading:

instead of .. minigallery:: matplotlib.pyplot.boxplot.

That way:

• we could limit ourselves to only giving Axes methods as references. (I see this as a plus, because in general we recommend the OO approach over pyplot.)
• Pyplot functions would still have a helpful minigallery.
• We don't need any customization in sphinx-gallery.

But up until somebody comes up with such a solution, we should go the manual route.

I think you can continue that discussion in #19232.