Okay so, first off, the download page:
https://www.oracle.com/ca-en/java/technologies/downloads/ (this is for Canada but it should either ask to redirect to the proper country or it doesn't matter; in any case, it's this page (country optional) you're looking for)
On here, select the JDK 21 tab, then the macOS tab of that one. It gives you 2 versions depending on your CPU architecture - to know which one you have, just go t the Apple menu > about this Mac and the processor will either say Intel (x64) or not (in which case, ARM64). Get the compressed archive for the correct architecture.
After that, did you download the most recent version of the ship editor? Iirc it doesn't ship with a bundled jre so you have to create the jre folder yourself. The folder should be on the first level of the Starsector Ship Editor folder, in the same place as the readme.txt, ship_editor.jar, etc.
At this point, you should be able to follow the instructions once again and everything should Just Work(tm).
You're probably not missing anything obvious; unless you have some good amount of programming experience and/or fiddling with a lot of stuff, most people wouldn't really be used to these kinds of procedures.