For the sake of God, please don't introduce a new global variable that is not a configuration setting; store in OutputPage, WebRequest or anywhere else you like, but not in the global scope.
You may also have a look at MediaWiki::getAction(); it doesn't do exactly what you request, but that's a first step.

Sure, sounds good. Changed the summary.

So it'd be implemented as something like MediaWiki::getAction or as a public method of a Request or Context object.

MediaWiki::getAction() returns the correct action and now writes it back to $wgRequest as well. I opened a separate bug for action diff as Bug 29840

Can this be closed?

Sure. If/when we're switching it all to be special pages, we can use SpecialPageName anyway, which is even better and has a canonical variant which is both available in CSS as well as JS.

Re-opening. MediaWiki::getAction barely, if anything, better than it was with getValue('action', 'view').

Using $mediaWiki->getAction() to determine mw.config's wgAction property or body class "action-..." is still unreliable as things like "/w/index.php?action=nonsense" will still make MediaWiki::getAction() return "nonsense".

The "real" action is determined in MediaWiki::performAction, which is using MediaWiki::getAction only as a mild suggestion to get started. We need to store the outcome of the performing action somewhere accessible from anywhere.

It is context/request dependent, but unless we can find a better place, how about storing the actual performed action (which will contain "unknownaction" if there was none, i.e. the "default" case of the switch() in MediaWiki:performAction) .. in a field of the MediaWiki instance and using a public getter to retrieve it?

Fixed by r108342.