You can farm fish outside territorial and exclusive economic zone waters. But in any event China has substantial EEZ waters: https://www.marineregions.org/gazetteer.php?p=details&id=848... Taiwan isn't much of a hindrance. For one thing, the Strait is 100 miles wide. And China's coast is much, much longer than Taiwan.
Check your map: with the exception a part of South China Sea that is a point of contention with Vietnam, China only has access to shallow water (For instance East China Sea is ~300m deep, which isn't significantly deeper than Norvay's Fjords).
On the contrary the eastern coast of Taiwan has access to very deep sea though.
(This is a well known geostrategic fact, as the small depths of Chinese water are a big weakness for their submarine fleet).