What do you do if it turns out that your product idea already exists?
There are some improvements I see, but it is very close to what I'd build, and it happened too many times already. I can't execute faster and I don't have enough resources. I got anxiety and depression because of this, but YC says that competitors don't kill startups and there are many startups basically doing the same thing, but they co-exist somehow. So what do I do?
They have validated the idea for you. Congratulations! And I can't imagine they are the be-all-end-all solution with no room for alternatives, are they?
Depends on your goal. Do you want to build a company or do you want to learn? Even if you have a completely unique idea, there's no guarantee that you'll find product market fit. Or maybe you have an idea that already has a market, but the current products aren't satisfying certain needs, or you think you can improve one aspect of the product.
I say build it, go at your own pace, and execute. The worst thing that can happen is you learn something.
Identify what type of market player the competition is and decide how you'll enter the market. If your competitor is a value play, for instance, you could focus on higher end market. What is your competitive advantage?
You should normally do it to solve your own problem. Does the idea solve it well enough or is there something missing?