Correct. At the moment the sleeve of the TRS plug (which carries the electric ground) is pressing against the second R of the TRRS input (which expects a Mic signal).
So the electric current from the electric ground is (falsely) understood as a Mic signal.
This Mic signal can not only carry sound, but also carry control signals from button presses (for example from the Cable Airpods.) Everytime you press a button on these things, a sound - outside of the human hearing range - is sent to the iPhone or Mac and interpreted as "louder", "softer", "play/pause".
Basically: Your Mac THINKS that you have cable Airpods connected to the TRRS adapter. And it THINKS that you are pressing buttons on your Airpods. Which - in the typical Apple way - brings up the Music app.
As far as I can see there is no way to stop the Music app from being triggered.
There is
one hack for an iPhone, but I am pretty sure that this can not be reproduced for your situation.
If you use a "proper" audio interface to record your cassettes this will not happen anymore. (Look at M-Audio M-Track Solo, €44 at amazon). Don't use the earphone out, but the Line Outputs on your Tape Deck. Much better Signal-to-Noise-Ratio.
If this investment is too steep for you and if you are satisfied with the result in Audacity, then I would simply ignore the Music app's behavior.
Also: Please ignore fisherman's advise. This has nothing to do with "Default Apps".
Good luck from a fellow sound engineer!