SAML with application privileges challenge

I have multiple applications with different authentication credentials (local authentication inside the app) Here SAML is the best choice in the APM right? and APM can uses LDAP auth and do credential insertion when communicating to the App server right?

Now suppose that : User 1 in appA has username USER_1 and password 123 while in LDAP has username User-1 and password 111

Now how SAMl will work here : If we keep the local app auth on, then the inserted credentials will be wrong and the server will refuse the auth.

If we disable the local auth, and depends only on the auth done by the APM, still we will not be able to manage the authorization and privileges for each user inside the application