How to enable Autoboot for old MacBook Air?
As you stated in your post, this is a feature of various 2016 (and later) MacBook models, it is not supported on your 2013 MacBook Air.

I suppose you could get into the habit of putting your MBA to sleep instead of shutting it down, as this would mean it'd start fairly quickly upon opening the lid, but of course that's not the same as auto boot.