You don't feel like you're good enough, but its not a competition
You’re not good enough and academia is too competitive. But it should never have been about competing. Look at the personal statement you wrote. Where is the sentence that says “I want to join the program to compete with others”?
You have been gifted (and I don’t mean you’re a genius, I mean they were gifts like birthday presents) with the ingredients for success. And that success is gaining knowledge and creating knowledge.
Publications, citations and retweets are just external metrics of this, as much as test scores are representative of a child’s academic worth. It has its point and it has its loopholes. And they matter more for your vanity rather than the true value of the knowledge you gain and you create.
Write a great paper with 0 citations? You gained knowledge. Write a shit paper with 10 citations? Don’t be ashamed as long as others gained something from it. Write a paper with 1000 citations? I’m happy for you, and I would not think any less of you if you hadn’t. But don’t forget the shoulders you stand on.
The universe has put you here, and asks only for you to gain and then return knowledge to humanity in good faith. Your ways of thinking, foraging patterns, technical background, resources, and community interactions will lead you down a certain mindspace. And if you go where no human mind has gone before, it’s a chance to give back so that someone else can stand a little taller.
Maybe someone would have built something “better”. But for whatever reason, the one who happened to wander into that space was you. You might be jostling for a while, and a while might mean years, but in the end you will find the knowledge that was always meant for you to find.
**Writer’s note; what I wish I could say to some of my friends, if ever I manage to frame it in a less obnoxious/preachy way.