If you're playing it via Spotify, it's not your music, it's Spotify's. Waymo is cool technology but I am disappointed at how the app requires a Google account plus access to google play services on an Android phone, and how the streaming music feature requires some kind of protocol that only Spotify and some proprietary Google music app support. All of my music is stored on a personal server that I stream to my phone via Jellyfin, and this does not work in a Waymo.
Yeah it was a little odd how I had to connect things, like I definitely would have preferred a simple Bluetooth connection so I could just play truly whatever is on my phone.