Does yoga actually help with stress, or is it just gentle exercise?

Both, and the combination is the point. Reviews find modest but consistent benefits for stress, anxiety and sleep, and the plausible mechanisms are real — slow breathing shifts autonomic balance, the physical practice reduces muscular tension, and the attentional component overlaps with mindfulness training. It is not uniquely superior to other exercise for mood, and claims about curing specific diseases are not supported. Where it stands out is accessibility: it needs no equipment, scales to any fitness level, and is culturally familiar here, which matters more for adherence than any marginal advantage in mechanism.