Yeah, like kolanaki said, you get softer bread and a better crumb with autolyzing (though it isn't the same thing as a bulk ferment). You also get more flavor.
Autolysing bread isn't the stretch and fold either.
It's the gentle mixing of the water and flour only, followed by a rest. This allows for better hydration, and some of the gluten development to occur. The enzymes in the flour make the gluten stretchier.
So, doing the stretch and fold is after autolysing. Doing it before bypasses the entire point.
That's the quick and dirty version, Here's the king Arthur write-up that's better
So, what you want to do is just mix the water an flour together, then let it sit. Only after that do you add anything else. No starter, no salt, no fats, nada. Afaik the only thing you would add during the initial mix is any tangzhong, if you're using that at all. But I've seen recipes that call for tangzhong to be added after autolysing as well, though afaik it shouldn't change anything either way.
Stretch & fold replaces kneading, and is often followed by a shorter bulk ferment before switching to a cold ferment (though that's getting into individual recipes, which veers off topic). If you knead, then you go to a longer bulk ferment.
Now, using a stand mixer for the initial mix is fine. You genuinely won't be able to detect a difference between a mixer being used for initial water/flour combination and doing it by hand. That's cause because you only mix long enough for things to be incorporated well. So it does the same thing, just faster. Where you'll run into a detectable difference (and it isn't that big a difference) is if you use a mixer instead of hand kneading. Using a mixer instead of stretch and fold, however, is very easy to detect as the gluten is a lot less forgiving, so you end up with smaller air pockets.