If they wanted to add a restriction to Action Surge, they could have simply changed a word or two in the same description to say it doubles your number of attacks in an attack action or grants an extra attack action. No, it pretty much writes point blank that you get an extra action (+ an extra bonus one, as well), which has no further restrictions. If they wanted to restrict it to attacks only, it would have been trivial to do it, right in the ability itself. I don't believe it's designed to be limited that way, and that's why I see it as the ultimate low hanging fruit for mages. It's funny that a barbarian would want action surge equally as much as a fighter might want reckless attack, but action surge doesn't limit the barbarian whereas reckless attack, well you're better off having Protector style if you want to live. Giving your foes advantage against you is a good way to die quick. Better use action surge when you reckless attack, whichever class is your main, lol. Yeah, I'm so not allowing multiclassing in my games where I DM. Except for my villains.