you can't moonwalk while you're in a run
you actually can't do a true "moonwalk" when you're in anything OTHER than an initial dash
that's because a moonwalk, by definition, is when you manipulate your momentum to slide backwards while still in the initial dash animation
the way to moonwalk the farthest (with basically any character) is to WALK in the direction that you're going to moonwalk in, then dash the OPPOSITE direction, and quickly half circle back in the direction that you were walking towards in the first place.
this way, the "walk" momentum stacks with your moonwalk momentum, and you slide super far to the other side. like arc said, if you're in a full run and you WAVEDASH then it puts you in a walk/slide/standing still animation, and you can moonwalk from there. this is probably what you're watching mango do, although there are a lot of extra trixies you can master, like crip walking like silent spectre lol.
honestly the best way to learn how to moonwalk (and in a broader sense, how walking/running momentum in melee works) is to play around with it on your own. you'll learn it the best that way