Well, right now it's just a wait and see what happens situation. I am really disappointed in the follow-up I received. The first follow-up request from the engineering team was for them to run a diagnostic on my phone (iPhone 11 Pro Max). It appears that they simply won't acknowledge the fact that everything was running just fine on iOS 12, and this began with the first version of iOS 13. They ran the diagnostic on my phone, and in the follow-up call 2 days later asked me to turn off the Wifi hotspot in my car (2020 Toyota RAV4), and then try CarPlay again to see if it solves the problem. Well, the Wifi in my car was not turned on, but I toggled it on and then back off anyway. Nevertheless, it still did not solve the problem. They said that if that did not solve the problem, send them a video of the problem occurring. I had already sent them a screenshot of the spinning wheel, but apparently that wasn't enough to satisfy them, so I sent a video. That was 3 days ago and I have not heard backs of yet. The 2 call backs I received were not from an engineer, but rather from a Senior Advisor relaying the messages from the engineering department.
At this point I am not very hopeful for a fix. I will probably end up discontinuing Apple Music and going with Spotify, but my new billing cycle just started, so I guess I'll stick it out for another month to see if there is a fix.