Well, I think it’s up to you which error code you’ll use. But if the actual functionality of your API depends on a third-party API, I would consider using the HTTP code 503 Service Unavailable, because your service will be unavailable until the third-party API works, no matter what HTTP code the third-party API returned. I would also include some details (error message) in the response payload.
Or you can return the HTTP code 200 OK and send the custom error code and message as the response payload, of course, because the HTTP request to your API was actually successful. But I would prefer to use the HTTP code to indicate the state of your API endpoint.
I would mirror the HTTP codes from a third-party API to the user only in case your API acts as a proxy without any additional functionality.