If I infiltrate someone else’s computer, secretly run code in order to to exfiltrate data I risk prison time because objectively it seems to satisfy criminal laws over where I live.

How do prosecutors in any modern country/state not charge this behavior when done by a website owner?

The difference is that there's implied consent to run arbitrary (albeit sandboxed) code when you visit a website. Moreover it's not the website causing the code to be executed, it's your browser. Otherwise if the bar is "code is being run but the user doesn't know about it", it would lead to either any type of web pages with javascript being illegal (or maybe without javascript, given that CSS turing complete), or a cookie banner type situation where site asks for consent and everyone just blindly accepts.