You would need a Bluetooth transmitter to send audio from the star to Bluetooth speakers. That box would connect to the star preout and just turn it on and off as needed. You would also need something to disconnect the star’s own speakers.
It’s probably easier to buy a muso and use Naim multiroom via the app.
I’d think a Muso, which could take advantage of the Naim multiroom streaming, would be dramatically better for kitchen listening, and would avoid the scourge of Bluetooth.