Hello Santhosh Singh (ext),
Thank you for posting your query in the Microsoft Q&A Community.
Your assumption that the Service Principal should inherit the "Contributor" role through its membership in an Azure AD group is correct. However, if the access is not showing up as expected, ensure that the correct Service Principal Object ID is used when checking for the assignment.
Alternately, go to the Resource group and list all the identities with access. If you still can't see the SP, assign a role directly to the Resource Group to check.
If this still persist after a while, I would advise you raise a Support Ticket for a more closer look.
Let me know if further assistance is needed.
Babafemi