It’s all about rights.
In short, you have the right to fish anywhere you like as long as it’s not a privately-owned place or places designated as ‘forbidden to fish’. Similarly, the military of the country that has the rights to the EEZ also has the right to tell you to shove it.
EEZ is not considered a nation’s sovereign territory. It is however, considered a sovereign nation’s economic rights. This economic right carries with it a heavy responsibility. The sovereign nation is expected to protect it and it is their responsibility to ensure that it is not littered with trash, pirates or terrorists.
What this means is while you can (in the strictest sense) fish in another nation’s EEZ, they can and quite often tell you to leave. Simply because if you fish in their waters, it means you are denying their own fishermen the ability to make use of those resources. If you’re just a single yacht doing your own thing fishing with a fishing rod, you’d most likely just be boarded and asked for identification papers, then told to go your own way after you’ve had your fun.
Seasteads however, is a whole other level. They’d be treated as a large fishing trawler, a commercial fishing vessel or even a smuggling vessel. Therefore, the nations would then exercise their rights to police and protect their own EEZ by giving seasteads the boot if seasteads are caught fishing in their EEZ. Some countries are more lenient, but most countries aren’t.
An example was when Indonesian navy opened fire on China’s fishing vessels that tried to fish near Natuna Island recently. Though that was probably political in nature, considering that China has been claiming every single island and atoll that their fishing vessels fish at, even where they have justification for the claim except “it’s an important fishing spot for our fishermen for generations” despite their fishing ships never been close to those regions until the CCP want those islands and atolls.