The key difference is the use of malted barley/hops for fermentation in production. If those are used (and probably some other requirements met, like being made in a brewery?) it can be classified as a Malt Beverage (a category that includes beer), putting it under TTB (who now regulate alcohol and tobacco moreso than ATF), and the correspondingly lax labeling requirements.

Most NA beer/Seltzers fall under this, and (my speculation from this point on) you probably won't see many N/A versions of the canned mixed drinks or vodka seltzers because they'd have to comply with a whole different set of rules since the NA version wouldn't be a Malt Beverage. Its possible that the Athletic/Partake examples you cite simply didn't see any benefit to getting certified as a brewery or added the nutrition label voluntarily, or were required to because they made some specific nutritional claim elsewhere on the can.

If coca cola wanted to make what was basically a soda, but integrate a fermented malt/hop component, I suppose they could maybe get away with that. But I think the TTB would shoot them down if it was a miniscule amount of malt/hop, and honestly I'm not convinced that it'd be at all worth the effort, since the facilities used would be regulated as breweries, and the formula would be subject to TTB approval, all just to avoid a nutrition label?

Another fun fact, it seems like beverages with no significant amount of any nutrient, vitamin, or mineral could probably get away without a label too. Not sure how hard that would be to achieve without just making it water though lol

See Slide 22 here: https://www.ttb.gov/images/pdfs/TTB_Boot_Camp_for_Brewers-_Nontraditional_Products.pdf

And the linked rulings from TTB: https://www.ttb.gov/images/pdfs/rulings/2008-3.pdf and FDA: https://www.fda.gov/media/90473/download