Allows to rotate an object around the target (a VR camera in my case).

RotationFollowSmooth.cs

using Sirenix.OdinInspector;
using UnityEngine;

public class RotationFollowSmooth : MonoBehaviour
{
    [SerializeField, BoxGroup("References"), Required]
    private Transform _target;

    [BoxGroup("Settings")]
    [SerializeField, BoxGroup("Settings/Rotation"), Required]
    private bool _followRotation = true;

    [SerializeField, BoxGroup("Settings/Rotation"), Required, EnableIf("_followRotation")]
    private bool _smoothRotation = true;

    [SerializeField, BoxGroup("Settings/Rotation"), Required, ShowIf("_smoothRotation")]
    private float _rotationSpeed = 5f;

    [SerializeField, BoxGroup("Settings/Rotation"), Required]
    private bool _mirrorRotation = true;

    [BoxGroup("Settings")]
    [SerializeField, BoxGroup("Settings/Position"), Required]
    private bool _smoothPosition = true;

    [SerializeField, BoxGroup("Settings/Position"), Required, ShowIf("_smoothPosition")]
    private float _positionSpeed = 5f;

    private Vector3 _initialOffset;

    private void Start()
    {
        if (_target == null)
        {
            Debug.LogError("Target not set for RotationFollowSmooth.");
            enabled = false;
            return;
        }

        _initialOffset = transform.position - _target.position;
    }

    private void Update()
    {
        if (!_followRotation) return;

        // Rotate the initial offset by target's Y rotation
        Quaternion rotationOnlyY = Quaternion.Euler(0f, _target.eulerAngles.y, 0f);
        Vector3 desiredPosition = _target.position + rotationOnlyY * _initialOffset;

        // Apply position (smooth or instant)
        if (_smoothPosition)
        {
            transform.position = Vector3.Lerp(transform.position, desiredPosition, Time.deltaTime * _positionSpeed);
        }
        else
        {
            transform.position = desiredPosition;
        }

        // Calculate the rotation to look at the target
        Quaternion targetRotation = Quaternion.LookRotation(_target.position - transform.position);

        // Apply mirroring if needed
        if (_mirrorRotation)
        {
            targetRotation *= Quaternion.Euler(0f, 180f, 0f);
        }

        // Apply rotation (smooth or instant)
        if (_smoothRotation)
        {
            transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, Time.deltaTime * _rotationSpeed);
        }
        else
        {
            transform.rotation = targetRotation;
        }
    }
}