Those are the things that work. You should try restarting your computer if you haven't.

https://www.zotero.org/support/kb/safari_compatibility#extension_not_showing_up_save_button_missing_or_flickering

I'm afraid there's no other answer. The plugin gets registered by macOS, not by us, and if it's not working, that's a macOS bug.

Make sure you have the latest version of macOS, delete the app from Applications, restart your Mac, redownload the app, and open the app. If the plugin doesn't appear in Safari after that, you may just need to use another browser with a more reliable extension framework.

(Also, did it work previously on this computer? Make sure you're looking in the right place.)

It's compatible — many people use it in Safari. But the Safari extension framework is just much buggier in general.

Again, though, you may just be looking in the wrong place. You need to go to “Safari” menu → “Settings” → “Extensions”, not “Safari” menu → “Safari Extensions…” It would be very unusual for it not to show up at all for a new installation.

Can you show the entire window? That doesn't look right.