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GH-36590: [Docs] Support Pydata Sphinx Theme 0.14.0 (#36591)

Preview: http://crossbow.voltrondata.com/pr_docs/36591/

### Rationale for this change

The Pydata Sphinx Theme that we use for our documentation has been pinned due to bigger changes in the theme layout. It needs to be unpinned and our layout needs to be updated.

### What changes are included in this PR?

Update of the Pydata Sphinx Theme and changes to our layout/structure:

- dark/light mode
- top menu bar
- search button in the top right navigation bar
- drop down from the theme layout in the top right navigation bar
- version warnings bar from the theme layout
- main landing page and the landing page for the dev docs

⚠️ Needs an update of the [versions.json](https://github.com/apache/arrow-site/blob/AlenkaF-patch-1/docs/_static/versions.json)

### Are these changes tested?

Yes, locally. Will also add docs preview via GitHub actions.

### Are there any user-facing changes?

No.

* Closes: #32451
* Closes: #36590

Lead-authored-by: AlenkaF <frim.alenka@gmail.com>
Co-authored-by: Sutou Kouhei <kou@clear-code.com>
Signed-off-by: Joris Van den Bossche <jorisvandenbossche@gmail.com>