We were having a similar issue where we had an embedded YouTube video for our current live stream and it was showing video unavailable even though we had the enableEmbed set to true.

This issue was fixed for us by changing the YouTube account setting found here: Settings -> Channel -> Advanced Settings Tab -> Do you want to set your channel as made for kids? this needs to be NO otherwise YouTube embedding will not work and will show Video is unavailable. Once this change was made our embedded videos were working as expected for live streaming