I'm not sure what to look for.
Does this problem only happen in GPU rendering?
Did you try OpenCL, Cuda, Optix?

Tried with optix, cuda and cpu, same result with all. Here's what the render looks like on my end, note the hard edges on the cube despite the principled volume in the cube having 0 density. The same issue happens if you have anything plugged into the volume material output for the small cube, including transparent bsdf

At first, I thought that small cube is refracting light somehow, but what happens here seems to be that density of small cube "overrides" density of large cube.

This picture is file as you provided

Here I moved right face of small cube a bit to the left.

As to whether this is correct behavior, I am not sure. This doesn't happen in eevee though.

I guess what you expect is some kind of volume blending?

I'm still pretty convinced there's something going on with how blender steps through volumes here, notice how in this blend file the stripy step artifacts become higher frequency and change direction inside the smaller cube in this scene, I recommend playing around with the viewport step rate slider for a good look at how the artifacts behave

how the render looks on my end, with the problems highlighted:

on how I'd expect it to behave I'd say volumes should interact cumulatively, where two volumes overlap the light gets scattered/absorbed by both volumes (without noticeable artifacting etc)

I have confirmed this on fact, that original file renders correctly in 2.82a. I have some problems to get consistent results with your new file so I am not sure what issue there is. it could be completely different issue