Hello @Cam Fisher,
Thank you for posting your query on Microsoft Q&A.
Based on the error message, it appears that the user account used during the installation does not have the required active role assignment in Entra.
In my testing, and as confirmed by the documentation, the minimum role required is Application Administrator. I successfully installed the Microsoft Entra Private Network Connector using a user account with an active Application Administrator role assignment (not an eligible assignment). However, when I attempted the installation with a non-privileged user account, I encountered the same error message you described.
I recommend verifying the user's role assignment in Entra once again. Ensure that the Application Administrator role assignment is active, as this is crucial for successful installation.
Please refer to the screenshot below for clarity.
https://learn.microsoft.com/en-us/entra/global-secure-access/how-to-configure-connectors
I hope this information is helpful. Please feel free to reach out if you have any further questions.
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Thanks,
Raja Pothuraju.