I don't work in medicine, but I was recently looking for a job in software engineering. I go to therapy every Friday afternoon and it's in a different city, so I can't work on that day, it'd be a nightmare to schedule.

I told them pretty upfront that I could only work 4 days a week and that I'd have to take Fridays off. All companies at some point asked why I didn't want to work full-time/what was going on on Friday. I told them that I have a regular doctor's appointment. Which is true since my T is a psychiatrist. They are not legally allowed to force me to answer what my condition is in that case. They asked me whether it'd impact my work while I'm there, but they didn't even ask about the specifics, what kind of doctor or what kind of illness.

I'd suggest not explaining why, and to at least if you are not too urgently required to find a job to choose to go every or every second week based on what you'd like better.
Once you start working there, know the people, everything, then you can still make the decision to tell them. But disclosing right away with what you struggle might make them less likely to hire you. Not because of the stigma, but because it's a risk for them and if another candidate does not pose that risk, they might choose that person. Since they don't know you, they can't tell what exactly depression means, does it mean sometimes just suddenly not showing up for work or is it no problem at all. So they might just go with the person who does not struggle with anything.

I don't live in the US, my country has significantly less stigma around mental health. Yet my T has advised me to not talk about what I'm struggling with during interviews. I decided to go with that and feel it was a good decision.