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Part I: Generate the version switcher JSON

You may want to look at this documentation first. In short, the changes under build_tools/circle/ are to extend the original script that generates the "All versions and download" page to also generate the version switcher JSON required by pydata-sphinx-theme. The generated JSON is saved at doc/versions.json and in conf.py this file is added to html_extra_path. It will then be pushed to https://scikit-learn.org/{ver}/versions.json. For now I'm using the JSON generated by the script, hosted under my website, so that maintainers can check how things work.

Part II: Tweak the version switcher (optional)

I think it might be nice to move the "Other versions and download" button in the navbar dropdown button into the version switcher, so that all version-related stuff are in the same place. My current approach is a bit of... hacky? Since the version switcher is itself populated by JS at load time, if we want to add another tab to the version switcher dropdown we need to use JS as well. More importantly to ensure the added tab is the last one we need to wait until the pydata-sphinx-theme script finishes. I've got no idea what the standard way is: my current approach is to add a listener to the dropdown button, hoping that no one clicks that button faster than JS executes 🤣. The JS is not too complex, but if maintainers think this is not desired I can revert to use the current "Other versions and download".

The banner looks good on the landing page:

or on the Examples index page:

however it's missing when navigating to a particular example of the gallery:

I also checked navigating to subpages of the narrative and API docs and the banner is there is both case. On the example pages have a missing banner.

Perhaps you haven't scrolled to the top (the breadcrumbs are not showing up)? If you navigate from the gallery index page to gallery example pages it jumps to the anchor on the header so the page is not automatically at the top; the banner only shows up when you scroll to the top (this is the pydata-sphinx-theme behavior).

Perhaps you haven't scrolled to the top (the breadcrumbs are not showing up)? If you navigate from the gallery index page to gallery example pages it jumps to the anchor on the header so the page is not automatically at the top; the banner only shows up when you scroll to the top (this is the pydata-sphinx-theme behavior).

Indeed you are right. Please ignore my comment then. I suppose this is good the way it is.

If the URL causes any issue I'll fix in a follow-up PR. Thanks @ogrisel!