You may have figured it out already, but you can reset the server by going into the account through which the server is currently authenticated (in your case, your personal Squarespace account) and removing the authentication under Account Settings >> Account and security >> Connected apps. You can then re-authenticate the server after logging out of your personal account in the browser.
How can you change the email that's being used when you include --auth flag on start server command?
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You may have figured it out already, but you can reset the server by going into the account through which the server is currently authenticated (in your case, your personal Squarespace account) and removing the authentication under Account Settings >> Account and security >> Connected apps. You can then re-authenticate the server after logging out of your personal account in the browser.