Game Object (BGM) persist through same scene, but stop on new scene

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I am struggling to write a script to perform the title objective.

I have 2 levels with a “BGM” object with the same script but a different audio source. Dying on a level reloads the scene and reaching the end loads the next scene on the build index.

basically i want the music to keep going when you die, but not on the next level.

Here is what I have so far for the BGM script:

using UnityEngine;
using UnityEngine.SceneManagement;

public class PersistSameLevel : MonoBehaviour
{
    int bi;
    static GameObject persist;
    int scene;
    void Start()
    {
        bi = SceneManager.GetActiveScene().buildIndex;

        if (scene != 0)
        {
            if (scene != bi)
            {
                Destroy(gameObject);
                persist = null;
                Debug.Log("not new, different scene");
            }
        }
        else
        {
            if (persist == null)
            {
                persist = gameObject;
                scene = bi;
                Debug.Log("new, no persist");
            }
            else
            {
                if (scene == bi)
                {
                    Destroy(gameObject);
                    Debug.Log("new, persist, same scene");
                }
                else
                {
                    persist = gameObject;
                    scene = bi;
                    Debug.Log("new, persist, different scene");
                }
            }
        }
    }

    void Update()
    {
        DontDestroyOnLoad(gameObject);
    }
}

I imagine a flow chart but cant seem to get the timing down.
if:
new and nothing leftover - stay
old and same scene - new is destroyed
old and new scene - self destroy and new one sees nothing leftover