unity – Make Minecraft Main Menu Camera movement

I intend to make exactly like this. I highly suggest you watch just 5 seconds of the video because it already explains what I intend to do. I’ve been trying cosine and sine on vector3s but I can’t seem to make it work since I usually get these results:

This however is my intended result:

This is my current code:

public class CameraWave : MonoBehaviour
{
    (SerializeField) float speed = 1f;
    // how deep and how wide the sine waves should be
    (SerializeField) float depthXY = 2f;
    // radius of the circle
    (SerializeField) float radiusZ = 10f;
    // makes the waves on the y axis and translates it 
    (SerializeField) Transform targetLookAt;
    // parent of target look at so we can move it in the z direction
    (SerializeField) Transform lookAtContainer;
    // set angle to middle
    float angle = 0.35f;
    Vector3 cameraOffset;

    void Start() { cameraOffset = targetLookAt.position; }

    void Update()
    {
        // adjust angle
        angle += Time.deltaTime * speed;
        angle %= 360;

        // make cos-sine wave
        float x = Mathf.Cos(angle) * depthXY;
        float y = Mathf.Sin(angle) * depthXY;
        // set to look at
        Vector3 position = new Vector3(x,y);
        targetLookAt.localPosition = position;

        // update container to make it go in circles
        lookAtContainer.position = MakeCircleZ(angle) + cameraOffset;
    }

    Vector3 MakeCircleZ(float angle){
        Vector3 v = Vector3.zero;
        v.x = (radiusZ * Mathf.Cos(angle));
        v.z = (radiusZ * Mathf.Sin(angle));
        return v;
    }
}

My hierarchy setup:

any help is appreciated