mediawiki.ui.button is used to style buttons in the content of a number of pages through the mw-ui-button class, typically as a call to action. It is the only major mediawiki.ui component used in on-wiki content, and we need a solution for this as part of deprecating mediawiki.ui.
In T346469, it is made clear that Codex components (and the CSS for the Codex Button specifically) is not guaranteed to be stable for use in wikitext. Unlike the many uses of mediawiki.ui components in code, an alternative plan will be needed for on-wiki content that does not rely directly on Codex.
This task invites discussion on a path forward that will still allow the deprecation and removal of mediawiki.ui (T182050), ideally without breaking existing uses or putting the burden of change on template maintainers in the short term.