Car steering on a Rigidbody (Mario Kart)

Hey there, I am fiddling around with a little Mario Kart like game in Unity. Currently, I am working on the car controller. I don't use Wheel colliders whatsoever, just a simple car model with a Rigidbody and Box Collider attached.

I managed ac/deceleration including the car to stop after a certain time (if no input by the user). However, I still can't figure out how to handle the steering.

What I want to achieve:

• Only steerable when velocity != 0, so only while moving forward/backward

• No or very little drag when turning

• Steering when driving backwards

Basically, this is what I am looking for: https://www.youtube.com/watch?v=ASWgJvuQhTA

My code until now:

 using UnityEngine;
 using System.Collections;
 
 public class kartcontrol : MonoBehaviour {
     private Rigidbody rb;
     private float inputX = 0.0f;
     private float inputY = 0.0f;
     
     public float currentSpeed = 0.0f;
     public float maxSpeed = 20f;
     public float acceleration = 10f;
     public float maxReverseSpeed = 10f;
     public float deceleration = 5;
     public float smoothStop = 5f;
     public float steeringAngle = 25f;
     private float velo;
     
     Quaternion targetRotation;
     
     void Start()
     {
         rb =  GetComponent<Rigidbody>();
         targetRotation = Quaternion.identity;
     }
     
     void Update()
     {
         inputX = Input.GetAxis("Horizontal");
         inputY = Input.GetAxis("Vertical");
     }
     
     void FixedUpdate()
     {
         if (inputY > 0)
         {
             // forward
             if (currentSpeed < maxSpeed)
             {
                 currentSpeed += acceleration;
             }
         }
         else if (inputY < 0)
         {
             // backward
             if (currentSpeed > -maxReverseSpeed)
             {
                 currentSpeed -= deceleration;
             }
         }
         else
         {
             // Stopping the car when no user input given
             var velocity = rb.velocity;
             var localVel = transform.InverseTransformDirection(velocity);
             currentSpeed = Mathf.SmoothDamp(currentSpeed, 0f, ref velo, Time.deltaTime * smoothStop );
         }
         
         // Apply currentspeed as rigidbody velocity
         rb.velocity += transform.forward * currentSpeed;
         Debug.Log(currentSpeed + " --- " +rb.velocity);
     }
 }
 

Thanks in advance :)