DOC: use the sphinx-panels extension for cards instead of raw html
This is an alternative for https://github.com/pandas-dev/pandas/pull/32065, using the https://sphinx-panels.readthedocs.io/en/latest/ extension (which was created inspired on how we are using this in our docs, but then nicely packaged in a sphinx extension to avoid the use of raw html).
@jorisvandenbossche still relevant? @jorisvandenbossche gentle ping This pull request is stale because it has been open for thirty days with no activity. Please update or respond to this comment if you're still interested in working on this. @jorisvandenbossche ? @jorisvandenbossche pls update or close @dsaxton I updated this PR to also convert the front page cards to use sphinx-panels, and with some custom styling to keep the same look and feel, I get this:

![image](https://user-images.githubusercontent.com/1020496/112748104-f65ddb80-8fb9-11eb-9ce4-df1b29902040.png)

The "buttons" are using the default darker grey and sharper corners from sphinx-panels, but if we prefer the lighter gray / more rounded corners as it is now, that's easy to change as well. 

For reference, screenshot of the current https://pandas.pydata.org/docs/dev/:

![image](https://user-images.githubusercontent.com/1020496/112748135-32913c00-8fba-11eb-821f-ec9e1932232e.png)
 > @dsaxton I updated this PR to also convert the front page cards to use sphinx-panels, and with some custom styling to keep the same look and feel, I get this:

Nice. The stronger contrast with the dark button color does make them a bit more readable. This is subjective though so I'm curious how others feel. +1 on the look and not using raw html