Release badge doc

What does this MR do and why?

Includes documentation work for the Latest release badge feature that we merged in !78899 (merged).

More details on the look and feel of the feature is available in the videos !78899 (merged)

Relates to #33368 (closed)

Screenshots or screen recordings

These are strongly recommended to assist reviewers and reduce the time to merge your change.

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.