I don't have a google home, but I have android TV (NVidia Shield) and an Android phone, Android Watch and several chromecast audios. Google Assistant on my android phone and watch can't interface with the chromecasts or android TV at all. I can "cast" from any app on the phone to most of the chromecasts, but not via google assistant. Android TV can't send audio to chromecasts at all, and it's a special snowflake that can't particpate in multi-room audio sent from an android device.

I have something called "google assistant" on all 3 devices, and none of them have even close to the same capabilities or UX flows for media playback, so I basically don't even bother using it because it's just frustrating.

This is because not all Chromecasts are created equal. If you have a "normal Chromecast" it works great, if you have an Nvidia Shield that comes with "Chromecast built in" it does not integrate with Home at all.