I made a mistake and I really want her back

So long story short, I made a mistake, I lost my job in the covid pandemic, I tried and failed many times to get a job and get my IT certifications, I eventually just got so depressed about it that, I acted like a child. I played video games, I woke up at 3pm, I drank alot, I treated it like a vacation. Then I became needy because she was the only thing I had to look forward to. I got so out of control she could not take it any more and left. To be fair I was the one that brought it up, but I now see that the reason I was unhappy and brought it up had literally nothing to do with her. It was me being needy and depressed. Now we did have disagreements, but I feel like majority of those disagreements were pretty normal, like deciding what to watch or where to eat, just silly things. So we broke up, within a week of us breaking up, I realized what I had become and I turned my life around. I now wake up at 4am to exercise, I have a full time job, I am a full time student, I am constantly studying for my certifications and passing my exams. I now realize this is the kind of life she wanted for me, but regardless of that for a moment, This is the life I wanted to live with her, I am progressing in life and I want to share these experiences with her. It took her telling me she had enough for me to get my stuff together. Now that I do, I cant help but realize how little effort I put into the relationship this past year, and I would love a life together with her. I did try to tell her this 3 weeks after the breakup, and that was a mistake and it was too soon. Now it has been 4 months, I feel as though we have both (or at least I) have calmed down and I would really like another chance to be the person she deserves. I have written a lengthy letter telling her how I fell, and I want to give it to her, but I also want her to be happy, but I don’t want to regret never giving a real attempt to revive the relationship. I am conflicted on what to do cause she was a once in a lifetime opportunity. I know I will learn to love again, but I don’t want to give up on this so easily considering a lot of the problems we had were my fault. Any one have any tips? if anyone has any more questions I would be happy to answer.