Safari browser extension won't unlock...

Hi BrendanJ
I had a scenario very similar to yours: family account, shared passwords and only one family member could not log in with his password in the Safari extension (on a macOS with all software in the latest versions).
Your post about being able to log into the extension with the master password made me understand what was happening here: the Safari extension was connected to my 1P login, not my family member's –– he was also able to log into the Safari extension with the master password when 'Integrate with the 1Password app' was disabled in the app.
I fixed it this way: in Safari, right click on the 1P extension icon > Settings. On the screen that opens, extension options, scroll down to "Accounts and Vaults" and notice the login entered. In my case, it was my email, not my family member's. So I logged out of that account and entered my family member's login.

Now, macos app and Safari extension have the same login again, and I was able to re-enable the "Integrate with the 1Password app" option.

Good luck!