IT looks to me like the truth is going to come out on its own when your grades arrive — or — you can find the courage to tell them the the truth. I think it’s better for you to do the right thing and admit that you dropped out of school. It will be difficult enough for them to realize that you are in so much distress without also having to handle the breach of trust that comes from lying about it.
You did have a reason. You didn’t set out to fail or to disappoint your parents. It sounds to me like it’s possible that you have been fighting with a depression and possibly a social anxiety disorder. I don’t have another information to make a diagnosis, of course. But what you shared in your letter does suggest investigating those possibilities.
Talking to your parents will be difficult. I do understand that and I sympathize. But not talking to them will be more difficult. So the thing to do is to try your best to tell them what has happened and why. You could start by showing them your letter (and this response).
You do need treatment. I don’t know what mental health services are available to you. Do check to see if your university has any mental health services for students like yourself. Many schools want to retain their students and will provide academic and psychological services to keep a good student on track. If face to face therapy sessions aren’t available, consider working with a counselor online. Other alternatives are outlined in the following articles here at Psych Central:
You could also consider what you can do to help pay for a private therapist.
Yes, this conversation will be difficult. Do work on keeping your defenses down. Be patient with their confusion and even anger. You’ve had months to think about this. They haven’t. The situation is a problem to be solved, not a reason to fight. You and your parents love each other. You are all smart adults. Working together, you can figure out what to do.
I wish you well.