The waveforms that you posted look like they were recorded at too high a signal level and that would cause distortion or “scratching the peak”. Once they are recorded that way, the damage is permanent, there is no going back (reducing the volume will not reverse the damage). But see https://forum.audacityteam.org/t/removing-crackling-from-already-edited-audio/59698/2
I am not clear on exactly what you are doing here. You seem to be playing the files from the network via VLC, and comparing that to a local recording on audacity.
Can you create a tone (sine wave) within Audacity? Will that play without distortion? If you save it as MP3, can VLC play it as well? Will it import back into audacity and play?