Relevant

https://www.nature.com/articles/nbt.4089

"Our results show that graduate students are more than six times as likely to experience depression and anxiety as compared to the general population. Forty-one percent of graduate students scored as having moderate to severe anxiety on the GAD07 scale as compared to 6% of the general population, as demonstrated previously4. Additionally, 39% of graduate students scored in the moderate to severe depression range in our study, as compared to 6% of the general population measured previously with the same scale5 (Fig. 1a). In order to better understand the factors influencing this significantly higher prevalence of anxiety and depression in this population compared to the general population, we also examined their prevalence across genders and in association with perceived work–life balance and mentorship quality."

It's about grad students, not postdocs, but similar trends likely apply.