When you use something like A extends B you are saying "I want to have something A that can be assigned to B".

What this means is that for typescript there are a lot of types that can be assigned to your interface I, you can see this with a simple example:

interface I {
    foo?: number
}

type TrueOrFalse = {} extends I ? true : false // true

This means that typescript has no way to automatically detect that a type assignable to I will contains the foo property, indeed:

hasTypeError<{}>({})

works just fine. This is why i.foo will still be typed as number | undefined.