Hello @Stephen Burgess,
Thank you for posting your query on Microsoft Q&A.
I understand that when you created an application through App Registration, an application object was also created under the Enterprise Applications blade. From there, you were able to configure claims using the Single Sign-On (SSO) settings successfully.
However, when you created a Microsoft Entra Application Proxy application from the Enterprise Applications blade, the Single Sign-On configuration prompted you to "Select a single sign-on method," which prevented you from configuring claims for that App Proxy application.
Both scenarios you described are expected behavior. When you create an application through App Registration, it typically uses the OAuth or OIDC protocol, so the SSO settings will appear as shown in your first screenshot. Conversely, when you create an application directly in the Enterprise Applications blade, the SSO configuration will resemble what you see in your second screenshot.
To add claims to your proxy application, you can select the SAML method under "Select a single sign-on method." This will allow you to configure the claims for your proxy application. You can add optional claims as needed under the "Attribute & Claims" section.
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.