This module is called "ICM2", the Infotainment Control Module (2), and it is basically a glorified control panel that talks to all the other modules (CD Player, Amplifiers, Radio, etc) in the car and tells them what to do.
Here I've documented the general experience of the reverse-engineering process, with pointers to more specific details to be found in my dedicated GitHub repositories linked in the sidebar.
I really appreciate the work you put into this, i was very close into changing this ICU into an aftermarket one, but now i have hope. there is one thing i think is not worth spending time, is that the main functionalities are rubbish, i wont spend time on switching between standard and custom. with the information you provided i think i will change mine too, but i will connect the arduino only to the 2 buttons on top right and the knob below (i do find that side also useless)
Again i want to thank you for the information you shared with us.