I agree with your assessment that your essay needs to have a more cohesive message and a stronger focus on why you want to go to this particular graduate program. Here are a few thoughts that I hope will help:
1. Your narrative makes you sound very naive and unsure of yourself. I like your story and I find parts of it that echo with me, but a story like this isn't a good story for your Statement of Purpose. I tell a story like yours when I talk to high school or undergraduates about my path to grad school and a research career. In a Statement of Purpose for graduate admission though, you need to have a different strategy. So, although you may not want to hear it, I think you need to re-write the entire thing to frame it differently. Remove all of the sentences that indicate self-doubt/naivete (also remove things like you were "lucky" etc.). This will help reduce your concerns of sounding "loosy-goosy". Next, I think you can add back in this doubt in one place: when you describe your decision to go for a MS first. If you balance it right, you can express a little bit of doubt and show that you make good professional decisions by considering what you want and then choosing the Masters route first. But now, you are ready to commit to a PhD program!
2. Your essay is currently all about the past. You're already at about 580 words according to a word counter. SOPs in our field tend to run around 750 words, so this leaves very little space for the real content of the SOP, which is "what you want to do, why, and why this school". Your background/history is meant to support the idea that you are qualified to do what you want to do, but it should not be the main focus. With the edits suggested above, it should cut down your text a lot, and I would aim for around 250-300 words on the background.
3. As I said above, you are lacking a strong thesis statement/argument in your essay. When I read it, it sounds like I'm just learning about your past, but I have no idea what you want to do in grad school. I would suggest that you start your essay with something like, "I am applying to the PhD program in X at University of Y to work on ABC". This immediately tells the reader why they are even reading your SOP. Follow this up with one or two sentences that expand on this. Then, the next paragraph could go back to your background. You would want to start your background section with a transition that links your previous experience with what you want to do (something like your current first sentence could work).
4. After your background, you want to go further on your goals in grad school. Generally, the prompt will expect you to write about what kind of topics you want to study, why these ideas interest you, and why this particular program interests you. You could name some people and describe some facilities/labs/etc. You should also talk about what your goals are in grad school (e.g. do you want to learn a particular skill? etc.) and what are your goals beyond grad school (something very general, do you want to do research in academia? in industry? engineering? teaching? something else?). For all of these goals, show why this particular school helps you achieve the goal. This section should be the main chunk of your essay, 300-350 words or so.
(Note: word counts are really more as a way for me to demonstrate how much time/focus to put on each topic, not meant to be taken literally).
Overall, I think your story tells me that you are ready for grad school and you are interested in pursuing a PhD. "Imposter syndrome" is common and many of us will try to downplay our achievements (e.g. by attributing them to luck) or focus on on what we don't know etc. But you are certainly capable of doing grad school, and focus on what you have done well! Good luck!