For clarification, in the support case, it was explained that you should intercept the SAML token to review the attributes and values returned by the identity provider. We pointed out to you that the group attribute being returned was using the object ID as its values so to get things working in Laserfiche Cloud for your federated group setup, with the current Azure AD setup, you would need to use those same object ID values instead.
However, please refer to the material that Sam was able to find from the internet which seems to provide the information you're looking for about how to get Azure AD to send back the group name in the SAML token. Then you can update the federated group configuration in Laserfiche and switch back to using the group name (after confirming that the SAML token is actually using the group name now).