EEZ and territorial waters, just like every other country on Earth

Not necessarily. That land was never a "part" of California. It was only ever part of the USA. It's weird to speculate that if CA left, it could also poach territory that is not currently part of CA and was never part of CA.

Feel free to show me an example proving me wrong, but I believe it is uncharted territory.

Why wouldn't California just, you know, keep the US's IP laws?

The US defends its IP laws and works hard to get other countries to acknowledge them via international treaties. If CA struck off on its own, at first, no one would recognize any of its international rights. It'd have to negotiate for those protections and that would take time. During the chaos of that change, companies reliant on IP would just hop over to the US because there isn't anything intrinsically holding them to CA.

Seriously -- ya'll need to read the Federalist papers 1-14 if you think CA (or TX or any other state) would be better off seceding. Ya'll ignant.