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Since it has been a week and the change is tiny, I took the liberty of pushing a commit with my suggestion and to fix the linting. Perhaps another maintainer can confirm this looks OK.

I think this doesn't quite cut it.

When embedding Matplotlib in a GUI, you must use the Matplotlib API
directly rather than the pyplot procedural interface. See
:ref:api_interfaces for an overview of Matplotlib's API interfaces.

The distinction in api_interfaces is between the "explicit Axes interface" and the "implicit pyplot interface". This primarily boils down to fig.some_func/ax.some_func vs plt.some_func. But what we need here ist the figure creation of bare Figure objects via fig = Figure() as opposed to managed Figures via plt.figure().

"the Matplotlib API" is too vague. Possibly the intention is something like

When embedding Matplotlib in a GUI, you must create standalone figure objects via fig = Figure() and not use pyplot-managed figures (plt.figure() or plt.subplots()).

The backgorund is that pyplot manages the window and eventloop, and that a GUI app wants to do this as well.

But there are also two funky examples (pyplot with GTK3/4), where the control is still left with pyplot, and we instead hack into the pyplot-managed window to extend it 🤯.

I see two options:

1. Either do something like my above recommendation, knowing that it's a bit over-simplified.
2. Or remove the block completely.

I'm leaning towards 2, since the gallery overview is not the place for coding specifics. Unforuntately we don't have a good place where the fundamental GUI pattern is explained. - There's more to it than just Figure(), it's also the Canvas and optionally Toolbars that need wiring up. It would be good to describe this as a tutorial at the example of one of the GUI frameworks. That should land either as first example in that section (maybe commenting on an existing example would be enough) or be a section in https://output.circle-artifacts.com/output/job/16c3ca48-942a-4d2e-9604-2d0be7802987/artifacts/0/doc/build/html/users/explain/figure/index.html.

Edit: Let's do it like this: Do 1. as an incremental improvement and create a follow-up issue for 2, which will remove the paragraph from the overview.