While there isn’t (yet) a complete gut health solution to depression it has been shown that, “…the composition of the bacterial community in the gut plays an important role in depressive symptoms.”
https://scitechdaily.com/new-research-shows-that-probiotics-can-help-alleviate-depression/amp/
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What is becoming more and more evident is that poor gut health is more prevalent in people with digestive issues and the microbiome is a possible FUTURE solution for depression.
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Until then, if you are on anti-depressants the science says to focus on gut health to help improve how you feel.