[docs] [docs infra] Finish Sphinx migration

[angelinalg]

Description

The Sphinx migration has been started but it needs to be completed. #35073
cc: @max

Link

No response

[peytondmurray]

I'm working on this in stages so the PR doesn't get overwhelming, and because there's a couple of different things we need to to make the Sphinx upgrade smooth. I'll add to this checklist as I go:

• Remove unnecessary doc dependencies. External modules for which documentation isn't being hosted shouldn't need to be installed to build the docs (e.g. tensorflow, torch, etc should be mocked out with autodoc_mock_modules)
• Attempt an upgrade to the latest version of Sphinx and all Sphinx-related dependencies. The docs will likely be broken/look very different due to changes in pydata-sphinx-theme and sphinx-book-theme. Determine the work needed to get the docs into a presentable state given the new styles.

[peytondmurray]

A few more todo items:

• We are dropping sphinx-external-toc, so there are a bunch of orphaned pages; we need to build a new toctree with these pages included to be displayed at the landing page for the docs.
• Move the CSAT widget out of a custom template. There's a pydata-sphinx-theme layout guide that shows where different things can be placed; the HTML for this can just be put in the sphinx configuration instead.
• Sort out syntax highlighting. In addition to pygments, we are also loading highlight.js in multiple places - without extra work highlight.js will not work for dark/light theme switches.