I have a family member who gets it due to anxiety and another one who gets it due to having sleep apnea and sometimes is overly tired to work long days at work 🤷🏼♀️
I've extended my FMLA due to anxiety. Plenty of people in my job have taken FMLA for anxiety and depression.
I haven't personally done it but I have a couple family members who have. Just make sure you have a doctor who will approve it before you even apply for the fmla.