I have had similar problems. Using my MacBook Pro with M1 chip.
Since software updates at the beginning of 2021 streaming from Apple Music to any airport unit is buggy and stops working after a few tracks. Only workaround seems to be restarting the computer, which is very impractical and annoying.
I have spent hours and hours with Apple Support, repeatedly going from staff who seem uninformed of the issue and then to Senior Technicians or advisors who eventually tell me Apple are aware of the problem and currently do not offer a solution.
The level of support has been extremely poor - uninformed staff, faulty phone consoles, not calling at times of arranged callbacks and not getting back to me for weeks unless I prompt them with emails. After years of happily using Apple products I am now at the point of advising people DO NOT buy anything with an M1 chip if they wish to stream music wirelessly.
Apple do not seem to care if they have customers who spend money on Apple Music plans and Apple computers only to realise they have had their money wasted.
I had been planning to also use my MacBook Pro with Apple Logic but this does not seem possible and I am forced to seek alternatives.
I am also now at the point that the process has been so frustrating I am going to cancel all my plans with Apple and use alternatives. As a long term customer and user they have totally let me down.