@Gary Kim Thanks for reaching out.
The authentication process for Dropbox API connection requires user interaction to grant consent for the application to access their Dropbox account. This is a security measure to ensure that the user is aware of the application's access to their data.
You could partially automate the process by using the Azure CLI or PowerShell to create the API connection and configure the necessary settings. Once the API connection is created, the user will still need to manually authenticate the connection through the consent page that pops up.
For more details on ARM template connection you can refer to this.
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