Pathfinding in 2d RPG

Hello, I am making a 2D RPG game, but I want it to be playable on mobile devices so you click on where you want the player to go but I don't want the player to go diagonally. That made a script that made the player go to the x axis first and then in the y axis.

using System.Collections; using System.Collections.Generic; using UnityEngine;

**public class PlayerController : MonoBehaviour { private Vector3 targetPos;

 // Start is called before the first frame update
 void Start()
 {

 }

 // Update is called once per frame
 void Update()
 {
     if (Input.GetMouseButtonDown(0))
     {
         Vector3 mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
         targetPos = new Vector3 (Mathf.Round(mousePos.x), Mathf.Round(mousePos.y), 0);
         ChackWay();
     }
 }

 void ChackWay()
 {
     Vector3 positionDifference = targetPos - WayChecker.transform.position;
     List<Vector3> moveProcess = new List<Vector3>();

     //first in x
     for (int i = 0; i < Mathf.Abs(positionDifference.x); i++)
     {
         if (positionDifference.x > 0)
         {
             WayChecker.transform.position += Vector3.right;
         }
         else
         {
             WayChecker.transform.position += Vector3.left;
         }
     }

     //then in y
     for (int i = 0; i < Mathf.Abs(positionDifference.y); i++)
     {
         if (positionDifference.y > 0)
         {
             WayChecker.transform.position += Vector3.up;
         }
         else
         {
             WayChecker.transform.position += Vector3.down;
         }
     }
 }

}**

Then I started using trees and things I don't want the player to walk through, so I used tilemaps and tilemaps colliers, and changed the script so that if you click on somewhere the player can't go by the first way it won't move.

using System.Collections;

using System.Collections.Generic;

using UnityEngine;

public class PlayerController : MonoBehaviour

{ public Collider2D terrain; private Collider2D coll; private Vector3 targetPos;

 // Start is called before the first frame update
 void Start()
 {
     coll = GetComponent<Collider2D>();
 }

 // Update is called once per frame
 void Update()
 {
     if (Input.GetMouseButtonDown(0))
     {
         Vector3 mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
         targetPos = new Vector3 (Mathf.Round(mousePos.x), Mathf.Round(mousePos.y), 0);
         StartCoroutine(ChackWay());
     }
 }

 IEnumerator ChackWay()
 {
     Vector3 positionDifference = targetPos - transform.position;
     Vector3 startPos = transform.position;

     //first in x
     for (int i = 0; i < Mathf.Abs(positionDifference.x); i++)
     {
         if (positionDifference.x > 0)
         {
             transform.position += Vector3.right;
         }
         else
         {
             transform.position += Vector3.left;
         }

         //waits until collisions are updated
         yield return new WaitForFixedUpdate();

         //if it is touching the terrain then it stops
         if (coll.IsTouching(terrain))
         {
             transform.position = startPos;
             yield break;
         }
     }
     //then in y
     for (int i = 0; i < Mathf.Abs(positionDifference.y); i++)
     {
         if (positionDifference.y > 0)
         {
             transform.position += Vector3.up;
         }
         else
         {
             transform.position += Vector3.down;
         }

         //wait until the collisions are updated
         yield return new WaitForFixedUpdate();

         //if it is touching the terrain then it stops
         if (coll.IsTouching(terrain))
         {
             transform.position = startPos;
             yield break;
         }
     }
 }

}

The problem is checking if the player is touching the terrain needs to wait for a fixed update and that means you wait 0.02 seconds every time you check if the player is touching the terrain. I also want the player to find a way to go to the point the mouse has clicked and go through the best path, so I searched on the internet, and I found a video that said you use A* algorithm and something like a grid system (https://youtu.be/waEsGu--9P8 and https://youtu.be/alU04hvz6L4), but it is difficult to understand (if it is only that I should just watch it a lot of times) and I want to understand totally the things I use on my game. The point is I don't know how to implement it with the tilemap and I don't want the player to move diagonally.

I would like to use the simplest way possible, even if it doesn't use the way in the videos.