DOC Update website to pydata-sphinx-theme

[Charlie-XIAO]

Reference Issues/PRs

Closes #28084. WIP.

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[adrinjalali]

@Charlie-XIAO you probably want to have a PR merging main repo's new_web_theme into main instead.

[Charlie-XIAO]

I was somehow trying to avoid myself accidentally messing up the main branch after I got the access 🤣 but okay I will reopen the PR from there.

[adrinjalali]

😆 yeah opening such PRs can be scary.

I personally have a separate clone locally which has write access to the main repo (my usual clone doesn't), to make it a bit more conscious when dealing with such PRs.

[adrinjalali]

Note that you don't have to do anything locally in this regard though. You can do everything through PRs to the new_web_theme of the main repo from your fork.

[Charlie-XIAO]

So essentially I should open a final cleanup PR targeting the new_web_theme branch, after which we should directly be able to merge new_web_theme back to main.

[adrinjalali]

The merging would also be through a PR, I opened it here: #29038, feel free to take over the PR. Once we're happy with the state of the new_web_theme branch, we simply hit merge on that PR.

[Charlie-XIAO]

Thank you so much!