Google Messages appears to be rolling out support for bubble chatheads as provided for in Android 11 Beta 1. The company promised this adaptation a few weeks ago.
Going into the app’s settings, users may find a new Bubbles item. Selecting it will take them to a system settings panel with the new interface for toggling on the chat heads.
As indicated from the promise in a comment by u/androidbetaprogram on Reddit, we were able to set up bubble notifications with beta v6.3.052 of the app — you can sign up to participate in the beta program here or download the specific version from APK Mirror. Sporadic reporting on this Reddit thread indicates that this may be a server-side push, though.