I have a TV with Chromecast 3 plugged in and an additional Smart Speaker (JBL Link 300). My Smart Speaker has a better sound quality so I would like it to be an audio output always, even if I ask it to play video music on my TV. Is it possible? Alternatively, I would like to play music on all speakers including a built-in TV speaker.
You will need to pair the Smart Speaker with the TV in some way for this to work. Modern TV's support Bluetooth headphones/sound bars.
I don't believe the Chromecast (This is the device actually doing the playback even when commanded via the smart speaker) can split it's audio output from the video, both of which will be output over the HDMI link.