I am not a plumber. My best guess is that at least some of the water to the apartment below runs through your walls. In my suspicion, the pipes are smallish, and generate noise. They are clamped in such a way that the vibration passes to your wall, which acts as a soundboard.
If the problem is the noise is being generated from inside your walls, you could have that path replaced with bigger pipes. You could put sound deadening material around the pipes.
For experiments, I would look at the noise when 3 gpm of just hot is used below. When 3 gpm of just cold is used below. Identify if the noise is strongest when a particular fixture is used -- does downstairs lavatory hot or cold cause the sound? Toilet refill after flush.
There are also sound deadening materials that could be applied outside of your wall surface. I am no expert on pipe noises, and I am throwing out things to consider and generate experiments.
If the noise is happening, and you have your sound meter going, does somebody pressing by hand at various spots on your wall reduce the sound?