Calculate shortest distance between two objects

Sounds like you need a Point-to-plane distance - For that you could use this method (c#)

 float distance = PointToPlaneDistance(smallObj.transform.position, wall.transform.position, wallNormal);

 private float PointToPlaneDistance(Vector3 pointPosition, Vector3 planePosition, Vector3 planeNormal)
 {
     float sb, sn, sd;
     
     sn = -Vector3.Dot(planeNormal, (pointPosition - planePosition));
     sd = Vector3.Dot(planeNormal, planeNormal);
     sb = sn / sd;
     
     Vector3 result = pointPosition + sb * planeNormal;
     return Vector3.Distance(pointPosition, result);
 }