Jump functionality for a 2D Top Down Unity game?

I am struggling to find an efficient way to let my player jump in a 2D Top Down world. I can see a lot of tutorials about platformer views where the camera is oriented at the side of the player, but nothing really working for a top down view like startdew Valley.

I am not using physics, so I move the character on the tilemap using a Couroutine which moves the player to the next position on grid, here it is my Update and DoMove methods:

    private void Update()
    {
        if (!isMoving)
        {
            input.x = Input.GetAxisRaw("Horizontal");
            input.y = Input.GetAxisRaw("Vertical");

            if (input.x != 0)
                input.y = 0;

            if (input != Vector2.zero)
            {
                animator.SetFloat("Horizontal", input.x);
                animator.SetFloat("Vertical", input.y);

                var targetPos =  transform.position + new Vector3(input.x, input.y, 0f);

                // obstacle detection
                Vector3Int obstaclesMapTile = obstacles.WorldToCell(targetPos - new Vector3(0, .5f, 0));

                if (obstacles.GetTile(obstaclesMapTile) == null)
                {
                    StartCoroutine(DoMove(targetPos));
                }
            }

            animator.SetFloat("Speed", input.sqrMagnitude);
        }
    }



    private IEnumerator DoMove(Vector3 newPos)
    {
        isMoving = true;

        while ((newPos - transform.position).sqrMagnitude > Mathf.Epsilon)
        {
            transform.position = Vector3.MoveTowards(transform.position, newPos, moveSpeed * Time.fixedDeltaTime);
            yield return null;
        }

        transform.position = newPos;
        isMoving = false;
    }

Is there anybody which could give me an hint on how to add a jumping feature? ( ideally with animation support?) I am kind of running out of ideas.

Thanks in advance.

Just think of it as animation only. Since it is 2D top down, it's more about it looking like it jumps, and then if it has to go over something while in the jump animation, test for just that. For example; if over hole and jump animation is playing, then allow movement over the whole, otherwise fall. So if the player presses the button for jump, the animation would play, and there should be some variable storing what animation the player is currently in.