Can I screencast to Chromecast at the same time as Bluetooth to a soundbar?

[cadmasterUK]

I have a Yaber V2 digital projector set up via a Chromecast dongle as a TV in Google Home. I can screencast my Galaxy Tab S7 to this but the inbuilt speakers are rubbish.
I also have a Samsung HW-J355 Soundbar and I can transmit YouTube sound to it by Bluetooth with no problem when I am watching the video on the Tab S7. But if I screencast to the Yaber, there is no sound from the soundbar.
Is there some way I can do both?

 

[fuzzylumpkin]

Is there a reason you can't just connect the soundbar to the projector? That seems like the most logical solution.