Google has been making some big changes to Google Assistant, such as moving the service to an app that can be downloaded from the Google Play Store and making it available on Android TV. However, it seems as though some functionality is being removed if reports from redditors are true.
These reports suggest that users were able to use Google Assistant to play music from their own library that was uploaded to Google Play Music, but a recent change now offers to play a streaming mix based on search criteria. Even setting Play Music set to return Downloaded Only music seems to have no effect.
The problem appears to stem from Google Assistant, not Play Music, as it never requests Play Music to play anything other than streaming content. Play Music, for its part does a good job and while it will queue what GA requests, will not download/stream anything new.
Several people replied in the comments affirming what the original poster cited, saying that they’re no longer able to request Google Assistant to play downloaded music when the feature worked just fine in Google Now.