I haven’t seen articles about this, but it comes down to this: your app needs a way to differentiate good churn (solved the problem) from bad churn (merely stopped using the app). An exit poll would be unlikely to get used by those whose problems weren’t solved, so you’d have to get more creative than that.

That said, in your case, I’m skeptical that you’ll have much hidden good churn in the early days. Depression seems like a long-lasting enough problem - and one that requires ongoing maintenance - that I’d defer this question until you’re receiving anecdotes like “3 months using your app has changed my life! Thank you!” every week (like dating sites do from people in new relationships). Make sure users know you value those stories. When emails like that start showing up regularly, like weekly, then maybe good churn is big enough to be worth trying to calculate. Also, you’ll have some actual examples that show how success manifests in app usage.)

(Obvious exception if your app is totally transactional, like a directory of therapists and all you do is connect the patient. If you’re providing help over time, some users will thank you if it works.)