DOC: Update pydata-sphinx-theme to 0.14
- [x] closes #55164 (Replace xxxx with the GitHub issue number)

<img width="1417" alt="Screen Shot 2023-11-08 at 2 08 28 PM" src="https://github.com/pandas-dev/pandas/assets/10647082/c76e6e39-7caa-4ef8-a96e-2f00539164f3">


Also uses a code block for an numpy operation that will change/fail with a newer version of numpy

I think you need to update `switcher_version` in conf.py to ensure it matches the version entries in versions.json file, to ensure the dropdown shows the correct version on the button. 
(from a quick look by downloading the artifact, that's not perfect because not everything works that way) > I think you need to update `switcher_version` in conf.py to ensure it matches the version entries in versions.json file, to ensure the dropdown shows the correct version on the button. (from a quick look by downloading the artifact, that's not perfect because not everything works that way)

Hmm I'm not familiar with how the version switcher works (or if it's supposed to work locally) so could you explain the specific issue? Going to keep this for the next release (I still have to test it locally a bit more for the switcher version), so broke off the numpy code block change to https://github.com/pandas-dev/pandas/pull/55911 > Hmm I'm not familiar with how the version switcher works (or if it's supposed to work locally) so could you explain the specific issue?

It's difficult to test locally (you need a released version to see it in practice), but so I pushed a commit that I _think_ will make it work, based on my knowledge of fixing it for arrow. 
Essentially, for the latest theme version, for the dropdown button to know which version of the docs you are currently viewing, it matches the "version" key in the json file with the `"version_match"` variable set in conf.py. And our json file uses short version numbers like "2.0" and "2.1" etc, so we need to update the variable we set as the current version of the built docs to something that matches that.  The light/dark theme switcher also seems to be missing > The light/dark theme switcher also seems to be missing

So looks like the light/dark theme switcher is still in the html

```
        <div class="navbar-item">

<script>
document.write(`
  <button class="btn btn-sm navbar-btn theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
    <span class="theme-switch nav-link" data-mode="light"><i class="fa-solid fa-sun fa-lg"></i></span>
    <span class="theme-switch nav-link" data-mode="dark"><i class="fa-solid fa-moon fa-lg"></i></span>
    <span class="theme-switch nav-link" data-mode="auto"><i class="fa-solid fa-circle-half-stroke fa-lg"></i></span>
  </button>
`);
</script></div>
```

Locally I had to comment out the `html_theme_options["switcher"]` for it to render correctly, so I'm not sure why it is interferring with the light/dark switcher /preview No preview found for PR #55885. Did the docs build complete? The preview seems to have worked: http://pandas.pydata.org/preview/55885/docs/ I see a few glitches I would report upstream, but I suppose this is good enough to merge for the RC. We still have some time to fixup a few things before the final release