Can a soldier in the barracks sell snacks and drinks to other soldiers in the barracks for profit, that were bought at the commissary?

There's a couple of competing issues here.

First, ANY time you are soliciting money from Soldiers at a workplace or federal building, there are ethics laws that come into play concerning funding. Even your company training room store, FRG fund raisers, and SAMC non profits have to abide by federal laws and ethics guidelines because they are soliciting money on federal property. Every one of these requires a JAG review when a new chapter or group is created and there is no SOP in place.
Second, you are not a store or an official business. That means you are running an unofficial, unlicensed business from the barracks. While the NCOs might not care, they don't have to take responsibility for it either. Once someone mentions [complains] to the commander, the CDR will be forced to give the yay or nay to your side business. He will have to ask himself, "if I approve of this, could it blow up in my face?". The answer to that is yes, a hundred different ways, yes.
There is also the AAFES non competition clause you mentioned, and yes that is a real thing. Of course, you're only competing once you are an official business

SPC (Join to see) Great advice has been offered by SFC (Join to see). I would not go forward with this plan without command approval, and you can expect it to be disapproved.

SPC (Join to see) to amplifÿ what SFC (Join to see) has said, you have a number of things that are really wrong here.
1. All commercial activities on an Army Installation require approval by permit or memorandum from the Garrison Commander or their designate, usually the Business Officer at FMWR. Especially on unit property. Usually people's side hustles are in public places (like a personal trainer or car detailer) or at their Government Quarters where utilities costs that are in excess, may be recovered.
2. DECA and AAFES items are not for commercial resale. One exception.
3. Units, operative word units, may run a "sweet and treat" snack stand among other fund raisers (similar to what you are doing) but any profit must be deposited in the account of the Unit Fund, run by your commander and administered by FMWR for unit morale and benefit. Those benefits must be available to ALL unit members (usually a BBQ at Organizational Day or Unit PT Shirts). Subject to legal review and audit at anytime. There is actually a SOP template out there provided by FMWR to run such a fund. The funds may be use due to replensih stock. The exception to #2is Unit Fund Raising i.e. The "sweet and treat" and FRG BBQs etc. two different regs and Fund instrumentalities in the nonappropriated Fund lanes.
4. Given installation policy, you probably have to have command permission for a second job, aka moonlighting, aka side hustle.

There are 4 or 5 separate regulations at work here. Your NCO ambivalence will not protect you when it goes bad, although, they should know better. All it takes is one guy to complain and they will swoop in and crush you. The people who knew and even bought your stuff will deny all knowledge.

Nothing will get a Commander riled faster than threat of relief for an illegal Fund. Do what your rank can stand. I don't have time to hunt down each reg for you but you need to hit the I believe button on what I have told you. If it is critical to morale and there is no significant profit, let the commander authorize you to run it.