This is an ancient that library that was introduced before 2010, and hasn't been touched since. It had one usage in WikiEditor where it iterated over queued up toolbar init functions asynchronously, which was unnecessary, and could also be achieved with promises.
Issues (fixed)
$ mwgrep "jquery.async" commonswiki MediaWiki:WatchlistMessageCreator.js (total: 1, shown: 1) $ mwgrep "eachAsync" bnwikibooks MediaWiki:Gadget-Special characters.js commonswiki MediaWiki:WatchlistMessageCreator.js enwikibooks MediaWiki:Common.js/Toolbox.js enwikibooks MediaWiki:Gadget-Special characters.js (total: 4, shown: 4) $ mwgrep "whileAsync" (total: 0, shown: 0)
Timeline:
- Deprecate in MW 1.33
- Remove in MW 1.34.