Hello @Ash,
Please note that in External tenants, supported account types for creating Application Registration is only Single tenant.
Please refer to the below Screenshot for your reference.
Please note that currently using Microsoft accounts and Microsoft Entra accounts as an Identity Provider is supported only for Invited Guests and not supported for self-service sign-up users(consumers and business customers) in External tenant and in Workforce tenant, using Microsoft accounts and Microsoft Entra accounts as an Identity Provider is supported for both self-service sign-up users(consumers and business customers) as well as for Invited Guests.
Please refer to the below Screenshot for your reference.
So the best approach will be to use custom OIDC federation as an External Identity Provider for self-service sign-up users.
Please refer to the below documents which will be helpful.
Add OIDC for customer sign-in - Microsoft Entra External ID | Microsoft Learn
Add MSA for customer sign-in - Microsoft Entra External ID | Microsoft Learn
I hope this above information provided is helpful. Please feel free to reach out if you have any further questions.
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