Can anyone help with my Camera Transitioning Issue?

I have got it running the way I want but the transition between player and camera movement are off the player is bouncing backwards when hitting the transition point. Can someone go over how I can resolve this issue or point me in the right direction please?

It is a 2d game and I would like the movement like that of the original Super Mario Bros.

I have tried several things like changing the offset value, giving the camera a speed value and a few other things I could think of trying but nothing seems to work properly.

[SerializeField] GameObject player;
    [SerializeField] float offset = 8.0f;

    private void Update()
        if (player.transform.position.x >= offset)
            Vector3 cameraPos = new Vector3(transform.position.x + 1,
            transform.position = cameraPos;
            offset = offset + 1;

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