How can I attach objects like a picture?

I'm not entirely sure what you're trying to do. At the moment it seems like you're just moving one object to another objects position, the reason they overlap is because you're telling them to share the same coordinates. There's a number of ways to make them sit next to each other, but it'll get more complicated the more complex your objects get. for now just try getting the scale of the object you're moving to and offset the first objects position by half of that scale.

  obj1.position = obj2.position;
  obj1.position.x/y/z += (obj2.localscale.x/y/z + obj1.localscale.x/y/z)

You can use this shader which offsets the drawn texture so that it is drawn a tiny bit more towards the camera, to solve the overlapping issue. Great for decals.

 Shader "Custom/BlendedDecal"
 {
     Properties
     {
         _Color ("Tint", Color) = (1,1,1,1)
         _MainTex ("Texture", 2D) = "white" {}
     }
     
     SubShader
     {
         Lighting Off
         ZTest LEqual
         ZWrite Off
         Tags {"Queue" = "Transparent"}
         Pass
         {
             Alphatest Greater 0
             Blend SrcAlpha OneMinusSrcAlpha
             Offset -1, -1
             SetTexture [_MainTex]
             {
                 ConstantColor[_Color]
                 Combine texture * constant
             }
         }
     }
 }