Turns out it has a fancy name, involuntary musical imagery. There’s even a scale for measuring it: https://www.gold.ac.uk/media/documents-by-section/departments/psychology/IMIS-pen-&-paper-version-&-scoring-info.pdf

Doesn’t look like anyone has figured out what causes it, but this paper provides some insights: https://www.frontiersin.org/articles/10.3389/fpsyg.2019.01904/full