DOC: Render the documentation with the website header and footer
Related to #28580, I think it should be quite quick, and add a lot of value, if we render the docs using the website header and footer, so the user feels it's always in the same page. It would also give more visibility to the home page (where the sponsor logos are), to the Contribute section (where the donation and other stuff to engage with pandas are), and to everything else in the website navigation.

Being specific on what I'd do:
- I'd remove the logo and the social media icons from the docs bar
- I'd remove the footer of the docs
- I'd change the base template of the sphinx theme, to the base template of the docs, so the website bar is on top of the docs bar in the final result

I think the main challenge is that the base template contains content that comes from the yaml settings, but that can be provided to sphinx in the settings. I think it can be done in an easy and clean way.

@jorisvandenbossche thoughts?