As a parent who has been on CC for many years, first child applied 5 years ago, and the second one your year, I want to tell you that what you are feeling is very normal.
My older one was deferred from Columbia when we all thought she should have been a shoo-in (we were a lot more naive back then). The night she was deferred, she curled up into a ball, with her head on my lap, cried herself to sleep. As a parent, it was the first time I felt there was nothing I could do for her.
Long story short, she ended up at Cornell. Just a week after she showed up on campus, she thought it was the perfect school for her, she didn’t know why she ever considered other schools, much less Columbia. She had very good 4 years at Cornell. She loved it so much, she really encouraged her younger sister to apply ED there this year.
Stanford’s admit rate is so low, with so many applicants, they probably could fill their class multiple times with very qualified students. I wouldn’t take the rejection as an indication of your qualification, maybe more of a fit.
I would get someone else to look at your application/essays again to see if there is anything you should change/improve. If you have good enough stats for Stanford, you will have many options come April, and end up at a place that’s right for you.
D1 wondered why she was rejected from Columbia when another girl from her school got in. It is something she would never know, but at some point it just didn’t matter any more. There is nothing wrong with you for feeling so bad. You worked hard to get to this point. As I told both of my kids, “Don’t let the college process define you as a person, and don’t let it diminish all you have accomplished.”
Good luck. Hope you feel better soon.