Camera controller: follow behind main character + offset

I use the attached c# script to control the camera.

Mouse scroll (pulley/roller/wheel): Zooming in and out of the main character
Up Arrow (or W key) and Down Arrow (or X key): Raise and Lower the camera
Right arrow (or D key) and Left arrow (or A key): Rotate the camera around the main character

I try to get the camera to follow the back of the main character, and add it the offset that player defined by using mouse and arrows.

This line correctly moves the camera according to the input from the mouse and arrows:

 transform.position = target.position + offset * currentZoom; 

This line correctly moves the camera so that it will follow the back of the main character:

 transform.position = target.position - target.forward + Vector3.up;

But each of them works correctly only if the other is canceled. If I try to merge them into one line, like:

 transform.position = target.position - target.forward + Vector3.up + offset * currentZoom;

then the camera doesn't move properly:

1. Using the left and right arrows moves the camera around the main character in ellipse/oval shape instead of in a circle

2. When the character moves, the offsset set by the right and left arrows isn't saved but the camera returns to being exactly behind the back of the main character

What do I need to do to combine the two lines so that camera does move properly?

 using UnityEngine;
 
 public class CameraController : MonoBehaviour
 {
     public Transform target;
     public Vector3 offset = new Vector3(10f, 6f, 0f); 
     public float RotationX = .5f;
     public float rightLeftSpeed = 5f;
 
     public float currentZoom = .13f;
     public float minZoom = .1f;
     public float maxZoom = 1f;
     public float speedZoom = .1f;
 
     public float currentHeight = 6f;
     public float minHeight = 0f;
     public float maxHeight = 10f;
     public float speedHeight = 1f;
 
     void Update()
     {
         currentZoom -= Input.GetAxis("Mouse ScrollWheel") * speedZoom;
         currentZoom = Mathf.Clamp(currentZoom, minZoom, maxZoom);
 
         currentHeight += Input.GetAxis("Vertical") * speedHeight * Time.deltaTime;
         currentHeight = Mathf.Clamp(currentHeight, minHeight, maxHeight);
         offset.y = currentHeight;
 
         offset = Quaternion.AngleAxis(-Input.GetAxis("Horizontal") * rightLeftSpeed, Vector3.up) * offset;
     }
 
     void LateUpdate()
     {
 
         transform.position = target.position + offset * currentZoom;
         transform.position = target.position - target.forward + Vector3.up;
         transform.LookAt(target.position + Vector3.up * RotationX);
     }
 }