Does exercise genuinely help mood, or is that overstated?

It genuinely helps, and the effect size for mild to moderate depression and anxiety is meaningful in reviews — comparable to some other first-line approaches, though not a replacement for treatment in moderate to severe cases. What matters practically: the effect appears at modest doses, aerobic and resistance training both work, and outdoor activity may add a little. The main obstacle is that low mood removes the motivation required to exercise, which is why starting absurdly small works better than a plan. A ten minute walk on a bad day is not a token gesture, it is the intervention.