If there were only one supplement to recommend, it would be magnesium glycinate: more than half of people may be running low, it's required for vitamin D to work properly, and a review of 18 trials suggests a possible benefit for anxiety, depression, and sleep.
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The core mechanism — magnesium is a required cofactor for the enzymes that activate vitamin D — is established biochemistry, correctly stated, and a point often missing from vitamin-D-only marketing. The "more than half" figure is reasonably close to US data (NHANES: nearly 50% of adults below the reference intake). The "18 trials" reference likely corresponds to a subset of a larger systematic review (32 articles, 18 specifically on depression) showing mostly positive but heterogeneous results on anxiety/depression, and a separate 15-trial review on sleep/anxiety points the same way. Overall this tracks a real, if nuanced, state of the research: a credible benefit, not universal, clearest in people who are actually low.
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