You'd get this error when using the Airtable desktop app. The initial login is not supported on the Airtable app. Only when using the browser. Please try to authenticate the miniExtensions form app by accessing Airtable from the web, not the native app. Then you can go back to using the app after finishing the authentication.
When you click "sign-in", a new tab should pop up. It is possible that your web browser is blocking the new tab from opening if you have an ad-blocker it could be preventing it. The fastest way to find out is by trying another browser and seeing if the problem persists.