It has been raised a number of times in the forum, that whilst casting/playing music on a Google speaker, any interruption such as a doorbell alert will stop the music and will not restart playing it again after the alert, I've linked a few topics below.
node-red-contrib-google-smarthome it's now possible to create alerts without even using tts, and which continue playing music after the alert.
As we can't upload mp4 files here, I've hosted a couple of quick videos on youtube as a demo (turn volume up!).
The first simply announces that someone is at the front door - https://youtu.be/CCvqQRJleHE
If you have camera recognition, you can also announce the name of the visitor - https://youtu.be/Xfk_nSrzpqo
Links to previous posts
Help, Google home return to play music after announcement?