I figured out the best way to work with that is having everything joined in the same object since the volumetrics work weird if they are in different objects, I don’t know why. Also, another thing that doesn’t work so well when you tint the liquid is the color of the surface tension area behind is stronger than it should. I saw some reference photos and it works like the changes I made.
On the left is the glass I modified, with no inversion of the inside juice normals, IOR of the glass: 1.5, IOR of the juice inside 0.87, IOR of the surface material 1.33. Inner juice and surface with a blue volume absorption with the density of 5.
I believe that could make your work a bit simpler.