It buys you:

Access to better treatment (even in countries with free health care, going private for mental health issues can help a lot)

Access to have more time to treat your depression (I.e. you don’t need to speedrun going through education or have to drop out completely, if you’re rich enough you can take time off and focus on getting help)

Access to more options for hobbies

The reduced mental pressure from stress of responsibilities such as paying bills

The lost goes on. At the end of the day, money doesn’t directly cure depression, but it can definitely indirectly help cure it, and other mental or physical health issues.

Bottom line - I’d sure as hell rather be depressed and rich than depressed and poor.