What is the connection between gut health and mood?
Real but frequently overstated. There is genuine bidirectional communication between gut and brain, and the microbiome influences it, but the evidence in humans is much earlier-stage than supplement marketing implies. What is reasonably supported: overall dietary pattern is associated with depression risk, with more whole foods, fibre, fruit and vegetables associated with lower risk. What is not established: that a specific probiotic reliably treats a mood disorder. A sensible position is eating well because it plausibly helps and definitely helps other things, while not substituting it for actual treatment.
Answers
Not substituting it for actual treatment is the important caveat here.
The honest 'real but overstated' framing is refreshing. Most content on this is selling something.