Guidance needed to understand quaternion and movetowards of gameobject - unity3d

Question

Hello I am trying to move a game object in 3d space I have searched the internet and found there are 3 ways to do that using turntoface(euler angles) or quaternion or navmesh agents
My problem is the game object default rotation is changing in using quaternions or move towards.
Can anyone help me understand why it is happening like that.
I want the capsule in slanted position.
//below code is using quaternions
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class Guard : MonoBehaviour
{
public float speed = 5;
public float waitTime = .3f;
public float turnSpeed = 90;
public Transform pathHolder;
public Transform target;
void Start()
{
Vector3[] waypoints = new Vector3[pathHolder.childCount];
for (int i = 0; i < waypoints.Length; i++)
{
waypoints = pathHolder.GetChild(i).position;
waypoints = new Vector3(waypoints.x, transform.position.y, waypoints.z);
}
StartCoroutine(FollowPath(waypoints));
}
IEnumerator FollowPath(Vector3[] waypoints)
{
transform.position = waypoints[0];
int targetWaypointIndex = 1;
Vector3 targetWaypoint = waypoints[targetWaypointIndex];
while (true)
{
Quaternion targetRotation = Quaternion.LookRotation(targetWaypoint - transform.position);
transform.rotation = Quaternion.RotateTowards(transform.rotation, targetRotation, turnSpeed * Time.deltaTime);
if (transform.rotation == targetRotation)
{
transform.position = Vector3.MoveTowards(transform.position, targetWaypoint, speed * Time.deltaTime);
if (transform.position == targetWaypoint)
{
targetWaypointIndex = (targetWaypointIndex + 1) % waypoints.Length;
targetWaypoint = waypoints[targetWaypointIndex];
yield return new WaitForSeconds(waitTime);
}
}
yield return null;
}
IEnumerator TurnToFace(Vector3 lookTarget)
{
Vector3 dirToLookTarget = (lookTarget - transform.position).normalized;
float targetAngle = 90 - Mathf.Atan2(dirToLookTarget.y, dirToLookTarget.x) * Mathf.Rad2Deg;
while (Mathf.Abs(Mathf.DeltaAngle(transform.eulerAngles.y, targetAngle)) > 0.05f)
{
float angle = Mathf.MoveTowardsAngle(transform.eulerAngles.y, targetAngle, turnSpeed * Time.deltaTime);
transform.eulerAngles = Vector3.up * angle;
yield return null;
}
}
void OnDrawGizmos()
{
Vector3 startPosition = pathHolder.GetChild(0).position;
Vector3 previousPosition = startPosition;
foreach (Transform waypoint in pathHolder)
{
Gizmos.DrawSphere(waypoint.position, .3f);
Gizmos.DrawLine(previousPosition, waypoint.position);
previousPosition = waypoint.position;
}
Gizmos.DrawLine(previousPosition, startPosition);
}
}
}
//below code is using turntoface (euler angles concept)
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class Guard : MonoBehaviour
{
public float speed = 5;
public float waitTime = .3f;
public float turnSpeed = 90;
public Transform pathHolder;
void Start()
{
Vector3[] waypoints = new Vector3[pathHolder.childCount];
for (int i = 0; i < waypoints.Length; i++)
{
waypoints = pathHolder.GetChild(i).position;
waypoints = new Vector3(waypoints.x, transform.position.y, waypoints.z);
}
StartCoroutine(FollowPath(waypoints));
}
IEnumerator FollowPath(Vector3[] waypoints)
{
transform.position = waypoints[0];
int targetWaypointIndex = 1;
Vector3 targetWaypoint = waypoints[targetWaypointIndex];
transform.LookAt(targetWaypoint);
while (true)
{
transform.position = Vector3.MoveTowards(transform.position, targetWaypoint, speed * Time.deltaTime);
if (transform.position == targetWaypoint)
{
targetWaypointIndex = (targetWaypointIndex + 1) % waypoints.Length;
targetWaypoint = waypoints[targetWaypointIndex];
yield return new WaitForSeconds(waitTime);
yield return StartCoroutine(TurnToFace(targetWaypoint));
}
yield return null;
}
}
IEnumerator TurnToFace(Vector3 lookTarget)
{
Vector3 dirToLookTarget = (lookTarget - transform.position).normalized;
float targetAngle = 90 - Mathf.Atan2(dirToLookTarget.z, dirToLookTarget.x) * Mathf.Rad2Deg;
while (Mathf.DeltaAngle(transform.eulerAngles.y, targetAngle) > 0.05f)
{
float angle = Mathf.MoveTowardsAngle(transform.eulerAngles.y, targetAngle, turnSpeed * Time.deltaTime);
transform.eulerAngles = Vector3.up * angle;
yield return null;
}
}
void OnDrawGizmos()
{
Vector3 startPosition = pathHolder.GetChild(0).position;
Vector3 previousPosition = startPosition;
foreach (Transform waypoint in pathHolder)
{
Gizmos.DrawSphere(waypoint.position, .3f);
Gizmos.DrawLine(previousPosition, waypoint.position);
previousPosition = waypoint.position;
}
Gizmos.DrawLine(previousPosition, startPosition);
}
}
This link has all videos and required output for reference