Throwaway for reasons...
This is not on you, regardless of how tormented you might feel. There should be no "what ifs" or "should have/could haves". This is mental illness, plain and simple. My story is not too dissimilar except that for whatever reason I didn't go through with the suicide.
A few years ago, as I was finishing up school anxiety and depression hit me like a ton of bricks. I had a 6 month old at home, unsure of a job situation, had done a few things that I wasn't and am not proud of. I started seeing a psychiatrist but the anxiety and depression was overwhelming.
I sat outside the doctor's office and started typing a goodbye email on my phone, which was basically the same as what your fiance had written - I want my daughter to be a better person than me and have a good father figure, I am not good for you, I don't deserve you, it's amazing to see how strong you are and you'll be fine. My parents, brother, sister, and friends were the furthest thing from my mind when I wrote this letter.
I knew I didn't want to kill myself at home since I didn't want her finding me, and I didn't want to go off in the wilderness for reasons. I walked down onto the subway platform with the email up on my phone, and stood at the back-of-the-train end of the platform (I usually stood at the front end of the platform) since the train would come in faster. I looked down the rest of the rush hour-crowded platform and thought about how awful a scene it would be for everyone who would have witnessed it and the train driver and decided not to do it.
Things have since gotten a bit better, but I still most certainly have my demons...
Please talk to someone if you're in my position or OP's, it can make all the difference.