During game-play, if you click on the MC's Smart Phone in the upper right corner, then click the "Music" Icon, it will load the "Hamster Player" Music App. From there it will show a list of ALL the songs in the game and along the bottom it will show the one that is currently playing.
Edit: Clarification & Typos.
That thought occurred to me, but there's no indicator on the song list which song is played where - just a plain alphabetical listing. This wouldn't be a problem... but the phone isn't accessible during the cutscene in question, which means there's no way of checking the Now Playing status. Hence asking if anyone knows which song it is, in hopes I won't simply have to guess based on the lyrics and go through that encyclopedic list. Thank you, though.
EDIT: found it. "Shake it Down" - an AI generated track by the dev. Ah, well.