However thanks to a recent server-side update (meaning that users won’t need to do anything on their end), songs that you’ve uploaded and purchased through Play Music can now be played through the speaker as well.
According to Google, “We wanted to share some great news! All your feedback and suggestions have been heard and we are happy to announce that you can now listen to music you’ve uploaded to and purchased on Google Play Music. On top of the subscription or free radio service, you can listen to music you’ve uploaded to and purchased on Google Play Music.”
Google also points out that there are certain limitations, such as how using your voice to play music and selecting the genre/mood/activity will not be supported for songs uploaded by yourself or purchased. There is also a longer command line if your default music player is not Google Play Music. The feature is rolling out to all Google Home devices as we speak, so do keep an eye out for it.