WEB/DOC: integration of the main website and documentation
With the new markdown based website (https://github.com/pandas-dev/pandas/pull/28014) and the new sphinx documentation theme (https://github.com/pandas-dev/pandas/issues/15556, https://dev.pandas.io/pandas-sphinx-theme/), we need to see how to integrate both. 

Roughly speaking, I can currently think of three options:

- Have them separate.
    - This is like we have it now, but of course styling-wise they can *look* unified. But the button for the docs on the main website goes to the doc website without actual integration of menus of both. 
- Also show the website navbar on the documentation site:
    - This would mean that when landing on the home page of the docs, you see two navbars: one of the main website, one of the docs. Once you start to scroll down, the navbar of the main website can eg disappear
    - An example of this is the docker docs (https://docs.docker.com/), where there are links from the main website fully at the top, which disappear when scrolling down (then only the navbar menu of the docs is kept).  
      I did a quick experiment for this: https://dev.pandas.io/pandas-sphinx-theme/pr-integration-website-double-navbar/. Right now this looks ugly of course due to the non-matching styles and alignment, but to give the idea and I think this can be made look nice with matching styles.
- Have a single shared navbar with menu items of both main website and the sphinx documentation site:
    - Just combining both as they are right now will probably give a too crowded header navbar, so we might need to make some choices what to put there. Currently we would have: Home, Install, Getting Started, User Guide, API Reference, Developer, Release Notes, Community, Donate. Probably Developer and Community could be combined, Release Notes is maybe also not needed on this level (the question is then where to put this though). 
      (TODO: will also do an experiment for this option)
    - Having the top-level navigation of the docs in a dropdown (so "docs" itself is only 1 item in the top navbar), as it is now at https://dev.pandas.io/, is also an option to reduce the number of items on the navbar. But personally, I think those should not be hidden in a dropdown, and one of the goals of the new sphinx theme was actually to make this top-level navigation more accessible.

Short term we can use the first option (eg if we want to start using the new theme on the dev docs this week), but I think ideally we want to go to a more integrated option? 

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Besides the choice on how we want it to look, there is also a technical issue to solve: how to put this common navbar in the docs? 
We can hardcode this in the html (when building it can eg be included in the layout from a file shared with the website), but this means that this navbar is fixed for older versions of the documentation, and if we do updates to the website this might not match with the header navbar of the released documentation.