Here’s a polyfill for the JS URL() interface which should give you a taste: https://github.com/zloirock/core-js/blob/272ac1b4515c5cfbf34... (I tried finding the one in Firefox but I couldn’t actually work out where it started, this one is much easier to follow)
TLDR: it’s a traditional parser—a big state machine that steps through the URL character by character and tokenizes it into the relevant pieces.
https://url.spec.whatwg.org/#url-parsing