RoadXY

So you can browse and search YouTube without starting the app?

I found out it's an Bluetooth profile called AVRCP (Audio/Video Remote Control Profile). As part of version 1.5 it's possible to browse the data on your phone. https://en.wikipedia.org/wiki/List_of_Bluetooth_profiles#Audio/Video_Remote_Control_Profile_(AVRCP) It did start to work when I had Google Podcasts and TuneIn installed which seemed to have support for this. Youtube Music (or at least the free tier) didn't support this.

I got this working on my work iPhone but not on my private Pixel 3XL. The iPhone 6 (old!) showed all music which I had available in Apple Music. It seems like it's baked in the Bluetooth media protocol but Android doesn't provide data (mine didn't). I did not have the Apple Podcasts app installed so when I selected podcasts in the console, it was empty. I then installed Apple Podcasts and selected a random podcast and downloaded the most recent, it was available in the radio.