One common reason for this behavior could be related to security settings or app permissions for your Gmail account. Sometimes, changes in these settings can affect how third-party apps like Mail.app interact with your account.
You might want to start by checking the security settings of your Gmail account. Log in to your Gmail account using a web browser and navigate to the "Security" or "Security and Privacy" settings. Review the settings related to app permissions and account access, ensuring that Mail.app is listed as a trusted app with the necessary permissions to access your account.
If you have two-factor authentication enabled for your Gmail account, consider generating an app-specific password specifically for use with Mail.app. This password can be entered in Mail.app's account settings to authenticate your Gmail account without requiring your regular Gmail password.
Additionally, make sure your Mac mini is running the latest version of macOS and that Mail.app is up to date. Software updates often include bug fixes and improvements that can address issues with app authentication and account access.
While you've mentioned trying to remove and re-add the Gmail account in Mail.app, it may be worth attempting this step again after ensuring that the other settings and permissions are correctly configured.
If the issue persists after trying these steps, it might be helpful to reach out to Google Support for assistance with Gmail account settings and security. You can also consider contacting Official Apple Support for further troubleshooting guidance specific to Mail.app and its integration with Gmail accounts.