Either you don't quite understand the purpose of a non-compete or there's an entire class of them I'm not aware of (which is entirely possible), but in my experience, their purpose is to explicitly bar employees from poaching customers from the business.

Working on something in your personal time that's similar to what you're working on for your employer -- unless your employment contract is entirely unreasonable -- isn't and shouldn't be a violation unless you are using company resources (including but not limited to trade secrets learned in the context of your employment and not legally available through other sources).