Stencil shader object "colliding" with outside of mesh

I think you want the water to look like it is inside your bottle with some width for glass thickness. You can achieve this by below steps:-

1) Make mesh just like the bottle. Add a material to it. To this material, you need to add new custom shader code { IMPORTANT when you add this Material with this shader, it will stop rendering on the scene. Do not think something went wrong. We want a masker which is just like a water bottle but a bit thinner so that we can see the glass thickness}

 SubShader
 {
         Tags 
         {  
             "RenderType"="Transparent" 
             "Queue"="Transparent"
         }
             Cull Off
         Lighting Off
         ZWrite Off
         Blend Zero OneMinusSrcAlpha

           Pass
          {
             Stencil
             {
                 Ref 6
                 Comp always
                 Pass replace
 
             }
             // blending zero to one will not render the object to the screen hence you can use this as a masker which is not rendered on the screen also
             Blend Zero One
     
         ***rest of the shader code***
          }
 }

2) Now to your liquid , you have to add a new material. Add a new custom shader to this material with this code

  SubShader
 {
         Tags 
         { 
             "RenderType"="Transparent" 
             "Queue"="Transparent+1"
         }
             Cull Off
         Lighting Off
         ZWrite Off
         Blend One OneMinusSrcAlpha
 
         Pass
          {
             Stencil
             {
                 Ref 6
                 Comp equal 
                 ZFail decrWrap                            
             }
                     ***rest of the shader code**
         }
          
 }