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.

Even company training room stores are not authorized as they can be considered a "slush fund", this is no different except it's even less innocent. You are reselling products for more than they cost at retail - pretty sure that's scalping - even if they are more expensive at the shoppette. The commissary is that cheap for a reason, and now you are undermining that government agency (DECA is the govt, AAFES is not - they just have a deal to be on post). I recommend you sell at the price you paid, or stop altogether. Doesn't seem ethical or legal, they're your fellow Soldiers, if you were honestly doing it to increase morale there'd be no profit.

WTF, you get snacks and energy drinks (and this much computer access) under supervision of a Drill Sgt?!?!?!?! What has the Army come to?

Considering that your customers are also your coworkers, one single piece of advice:
"You don't shit where you eat."

This isn't anything new. Every unit I was at there was a kid doing a side hustle and slinging something. Razors, snacks, drinks, DVDs, etc. The one common thing is that eventually the Command finds out and eventually it gets shutdown. It's not uncommon for units to maintain a soda mess, coffee mess or some form of small concession in a work space. But eventually something happens,somebody gets mad, money goes missing, it gets flagged and it goes away for a while and eventually pops back up when enough people from the original crew rotate out. It is a cycle and it goes round and round. Command has final approval on all side gigs and generally shut down inside ones like this. It's gonna happen. You can either try to get Command approval or wait until they shut you down outright but the odds are not in your favor.

Way back in the day I had acquired the collateral nickname HEBO; High End Booze Officer. I'd buy up all the good stuff during the Winter Fly-In to Antarctica. Since I had to audit the Package Store, the audit was much simpler. Then over the summer period, I'd gradually sell it off on a not for profit basis. That way, there were no hoarders or Stay a Whole Day Air Farce types raiding the store for good stuff. It was an open secret, so much so, I was the only O-1 that happened to get invited for dinner at the Skipper's hut most every week. He got a monthly bill. Where I'm going with this is can/can't do regulations aside, I advise nobody make hay off their shipmates, but rather take care of them. Your actions will get repaid nicely in interesting ways. It does take a Village to help people along. It only takes one Village Idiot to cluster everything up.

Back at RAF Lakenheath in the late 90's I ran the coffee bar at work, and I bought all the supplies out of my own pocket, then divided up the cost by the number of members. My boss made sure I didn't make a profit in case AAFES did get nosey about it.

Dang you all are a wild up bunch. This has gone on for the begging of time. If it isn’t class 6 or rationed items in countries that have them. Chill, I doubt he is competing against aafes.

Uh, just don't do it.