Makes a few changes to better align the update license API docs with
the [API reference template][0].
Changes:
* Replaces POST with PUT in several snippet examples.
While both are valid, PUT is a bit more RESTful.
* Removes leading slashes (/) from all snippets.
* Relocates and retitles the 'Authorization' section to 'Prerequisites'.
* Replaces explicit titles with the appropriate API reference template
attributes.
* Replaces unneeded `[float]` tags with explicit anchors.
Closes#35341
[0]: https://github.com/elastic/docs/blob/master/shared/api-ref-ex.asciidoc
James Rodewig
Lisa Cawley
Jason Tedor