At some point before things got at all serious I would want to know more about their history and how they have dealt with things. Those are good things to know about anybody you're considering a relationship with.
I would want to find out how much insight or self awareness the person had, but then I wouldn't want a relationship with anyone who was not very insightful or self aware. It would be frustrating and dull.
I would want to find out how much responsibility the person took for themselves, their behaviour and their health. Again, that's good stuff to know whoever you're dating.
I have a history of severe depression. In my case it's not in the distant past, my most recent bout was the year before last and I would be surprised if it was my last ever episode.
Would I date me now? Yes, I've learnt over the years how to tell if I'm getting depressed, what helps and what doesn't and when to seek outside help. While I will tell DP if I am feeling low, I don't expect him to be my nursemaid or to rescue me and make it all better. It's up to me to make sure I do my bloody exercise and get enough daylight and eat properly and drag myself out of the house and make contact with people and if I find myself unable to do that or it's not helping, it's up to me to take myself to the Dr's and discuss treatment options.
Would I date me in my early 20's? Hell no. I was a vortex of unaware, irresponsible destruction and I don't think anybody who dated me back then had my best interests anywhere on their radar.