How to receive OIDC client_id in external SAML IDP AuthN

I have multiple OIDC applications setup sharing a common custom external SAML IDP. There is a request to capture information about the application within an audit during the external authentication flow. I don’t see the client_id from the original OIDC authorize in the SAML AuthN request anywhere. Does anyone have experience with a requirement like this? Can it be added? Maybe it is there, and I simply don’t see it? Any help would be greatly appreciated,

From the application side, the ID token issued to the user that signed in via an external IdP will contain an ‘idp’ claim that will contain the ID for the external Identity provider (within the Okta tenant) they used to login. Would that work?