It has a positive affect on an irritated stomach lining, I've found. This is easy for me to explain when it's slime/phlegm doing it, as the bubbles helping enzymes and stomach acid dissolve the goo.
I'm seldom enough drunk to have a good sample, but liquor isn't good for the stomach, and I've cautiously drunk a pint of sparkling water with complete success, while knowing that still water would have come back up within five minutes.
Maybe the stimulation of the bubbles promotes the lining to exude what it's supposed to, which alcohol strips away? No idea but I do think it materially helps.
Plus mineral water does contain far more electrolytes than tap which I think has a non-zero effect
My secret? I was far too drunk to sleep when we got to the hotel so I stayed up drinking about 100oz of water over the course of an hour or so, while sobering up. Just drink water, you probably don't need the vitamin C, or if you somehow messed up your "electrolytes" or something, just sip gatorade.
Most of a hangover is dehydration, or not having enough excess water in your blood to easily expel the literal vinegar the metabolism of ethanol creates.