How does such a system sustain itself?

The majority of the content on the internet is supported by ads with the expectation that you, a human that has money, will consume something and spend money on them.

If people are replaced by some synthetic representation of themselves, what is the incentive to sell advertisements on the internet if there are no humans?

Fake/artificial traffic is a big problem today, it will be harder and harder to detect but its presence will be more and more obvious.