How does the audio visualizer work?

The Audio Visualizer is the little box on the bottom left of the screen whilst playing. When there is no music playing, it stays still, and when music is playing, it adjusts to the volume/beat/etc. of the sound.

How does that work? Is there a video file associated with each track that plays when the track plays, or is there some way that the game adjusts the audio bars to what is playing? If so, would it play differently to a custom track?

There is no video file associated with the music. You can easily verify this if you create a OGG Vorbis with no sound at all and replace all music in your Hacknet/Content/Music directory with that file.

Hacknet doesn't seem to verify that the files weren't tampered with, so you can replace the files with arbitrary ones, and yes, the audio visualizer will show something else.

As far as I know, Hacknet is written in C# and uses the XNA framework, which provides a class MediaPlayer, which again provides GetVisualizationData. If Hacknet uses both the MediaPlayer and the VisualizationData correctly, you should get a proper visualization of your (changed) songs.