How to make the camera follow the player while still being able to be rotated?

In a camera script, I want the camera to be able to rotate around the player on the y-axis. This works fine, but when I make the camera follow the player, it won’t be able to rotate because it’s constantly being set to a certain position. How can I make the camera follow the player, but still rotate around the player as well?
using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class CameraScript : MonoBehaviour {
    public Transform target; 

    public Vector3 offset;

    public float yawSpeed = 100f;

    private float yawInput = 0f;
    private bool mouseDown = false;
    void LateUpdate()
    {
        //transform.position = target.position + offset;
        transform.LookAt(target);
        if (Input.GetMouseButtonDown(1))
        {
            mouseDown = true; 
           
        }
        if(Input.GetMouseButtonUp(1))
        {
            mouseDown = false;
        }
        if (mouseDown)
        {
            yawInput = Input.GetAxis("Mouse X") * yawSpeed * Time.deltaTime;

            transform.RotateAround(target.position, Vector3.up, yawInput);

            

           
            
            target.gameObject.transform.rotation = Quaternion.Euler(0, transform.rotation.eulerAngles.y, transform.rotation.eulerAngles.z);
         
            

            print(target.gameObject.transform.rotation.y);

           
        }
     

    }
}

Thanks!

I suppose by the Y axis you mean to rotate AROUND the player, not going up and down, neither getting closer or further.

I’ll do it by having a transform poiting to the the angle we are looking from the player (0 is we’re facing him, 90 is besides, 180 is on the back), than going forward, making at look at the player, than making it the camera transform.
I didn’t test the code but i think it Works. Anyway i made my point.

    using UnityEngine;
    
    public class CameraTrack : MonoBehaviour {

    public float rotateSpeed=4.0f;    //Time in seconds it takes for the camera to rotate around the Player
    public float distance=4.0f;    //Distance from the camera to the player

    Transform player;    //Make the camera a child object of the player in the inspector

    Transform auxT;
    float currentRot;

    void Start(){

        player=transform.root;

    }

    void Update(){

            currentRot += (input.GetAxis("Mouse X") * (360/(rotateSpeed*time.deltaTime));
            currentRot %= 360;

            auxT = player;
            auxT.rotation.y = currentRot;
            auxT.position = Vector3.forward * distance;
            auxT.lookAt(Player);

        }

        transform = auxT;

}