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:D

Wow! Cool update :)

This is a really good idea! Thanks!
The implementation contains some nuances:

Input.mousePosition return pixel coordinates. It needs to be converted to virtual coordinates.

// Moving player to left and right
void MovePlayer()
{
    // Get mouse position in pixel-coordinate system and transform it to virtual-coordinate system
    Ray mouseRay = camera.ScreenPointToRay(Input.mousePosition);
    mouseX = mouseRay.GetPoint(10f).x;
    if (gameManager.isGameActive)
    {
        if (mouseX < leftBound)
        {
            positionX = leftBound;
        }
        else if (mouseX > rightBound)
        {
            positionX = rightBound;
        }
        else
        {
            positionX = mouseX;
        }
        playerRb.MovePosition(new Vector3(positionX, playerPosY, playerPosZ));
    }
}

The project has updated. You can test it.

Added a link to you in devlog ;)

I just set the high "Horse Power" (25000). For this course, this is an acceptable solution.  I was interested in this question and I found a good video demonstrating the implementation of the car.

As a quick fix, I used WheelCollider.motorTorque:

// Remove force from the car
// playerRb.AddRelativeForce(Vector3.forward * horsePower * forwardInput);
// Add motor torque to the wheels
foreach (var wheel in wheels)
{
    wheel.motorTorque = horsePower * forwardInput;
}

This gives a more correct behavior to the car.

Sorry for my English, I use Google Translate :)

Good implementation. But the car moves back and forth with respect to the global coordinate system. If you use the AddForce method to move forward, try replacing it with AddRelativeForce ;)

Thanks. Indeed we are the only ones)