Yes, coastal waters belong to the adjacent US state
The Federal government has jurisdiction over “admiralty and marine” matters from Article III of the Constitution. Which decisions of the Supreme Court in the 19th century over marine vessels and navigable waters. This is broader than English law where admiralty law ends at the high tide mark, giving the Federal government jurisdiction over navigable rivers and lakes.
In the judiciary act of 1789 this power was given to the Federal district courts “saving to suitors the right of a common law remedy, where the common law is competent to give it." Which effectively gives joint jurisdiction between that court and competent State courts because a “common law remedy” means any civil dispute that is not carved out by Federal law.
Criminal law is more complex. A state (national or sub-national) has jurisdiction through one of 4 internationally recognised principles:
- territoriality, where it happens in the state’s territory (inland waters and the 12 mile limit,
- nationality, where one of its citizens is the victim or perpetrator,
- universality, where the crime is heinous and condemned in all nations,
- protective, to protect its interests.
It doesn’t take much imagination to see that many states can have jurisdiction at the same time. Basically, it’s a confusing mess which leads to a “can’t somebody else do it?” Attitude that makes much of the worlds oceans practically lawless.
- Do I have to pay California taxes?
- Can I have on the boat a rifle that's allowed in US but banned in California?
If it’s permitted by Californian or Federal law, it’s permitted.
- My doctor is license to practice medicine in the state of California. Is it legal for him to treat me on board?
Yes because you are in California. Also if they are allowed by the port of registration of your vessel because this is allowed under international maritime law.
- Can LAPD enforce LA city ordinances on my boat?
I don’t think so but only because I think the county boundary ends at the shore. California local government is as confusing as maritime law. You are probably under the jurisdiction of the Port of Los Angeles.
- Can my kids, whose primary residence is my boat, attend public schools in LA school district?
No idea. Probably?