API docs: web: add 'Experimental' badge, feedback/docs buttons

Created by: slimsag

This change adds a floating 'Experimental' badge to API docs pages, as well as feedback/learn-more buttons:

The feedback button opens our feedback widget, and the buttons follow you as you e.g. are further down on the page:

Fixes #21923 (closed)

Fixes #22436 (closed)

Signed-off-by: Stephen Gutekanst [email protected]