This is incorrect. Most ATP found in our cells is in the form of MgATP and magnesium is crucial for the regulation of ATP production [1]. ATP levels are tightly controlled within cells and although mitochondria may play a role in psychological disorders [this article][2] simply saying that less ATP means less anxiety is wrong.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4960558/ [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5997778/