So does this mean we're stuck with the USB-C form factor forever? If no device can have a different connector how do we ever get to what comes after USB-C?
No, but it might mean we're stuck with USB-IF forever. Which, on balance, is probably the best reasonable outcome. USB-IF as an organization, and the standards they put out, have many flaws. But it's the most widely adopted, has the most members, and is still relatively open. Balancing that with the desire for standardization, I'm not sure we could have done better.
Remember that USB-C is just a physical plug. Many different protocols and interfaces can use the USB-C connector, and many of these protocols and interfaces require specialized cabling. This new law doesn't hinder whatever protocols, interfaces, or cabling that comes next - as long as they continue to use the USB-C connector.
And if there does come a time when the USB-C physical plug itself is the limiting factor, I am sure USB-IF will come up with a backwards compatible next plug while at the same time pushing the EU to update their regulations.