Are audio cassettes FM or AM?
Neither, there is no modulation involved. The magnetization on the media is directly (and hopefully fairly linearly) related to the waveform amplitude.

There is a high frequency bias signal added to the audio signal, to get the resulting signal on the tape to a linear range of the magnetization curve, but the signal at the head is a sum of the two, not a modulation.



That image is from here, a good description of the process. This is stressing my memory of tape decks I had 40 years ago...  The one instance I recall of amplitude modulation (kinda) was Dolby HX, which changed to amplitude of the bias in response to high amplitude audio signals, to keep the resulting signal from going into saturation. https://en.wikipedia.org/wiki/Dolby_noise-reduction_system#Dolby_HX/HX-Pro