It sounds like there may be a couple possible issues here, then. First, connecting the CCwGTV directly to your TV means using the ARC (audio return channel) feature of HDMI to get the audio from the ...
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It sounds like there may be a couple possible issues here, then. First, connecting the CCwGTV directly to your TV means using the ARC (audio return channel) feature of HDMI to get the audio from the TV down to the sound bar. Regular ARC can't carry 5.1 channels of PCM (uncompressed) audio, and Stadia uses a low-latency compression scheme that will be decompressed to PCM by the CCwGTV and sent using the regular audio channel on HDMI (which can carry all 5.1 channels uncompressed). So, you have 5.1 channels of PCM coming from the CCwGTV into the TV, but no way to get all of that down to the sound bar via ARC. I suspect the TV may be picking just the left front and right front channels to send down to the sound bar via ARC as stereo audio (more on this below, though). There is a newer version of ARC called eARC that can carry that, but both the TV and the sound bar would need to support that.
The second thing I notice here is that you said you were experiencing this through the TV speakers prior to adding the sound bar. This makes me suspect the TV may be picking off only the front left and front right audio channels from the 5.1 channels coming from the CCwGTV. For the TV speakers, it should be mixing all of these channels together to get left and right stereo audio. But, the TV may simply not be capable of that. Even if it was, it would only be able to send that stereo signal down to the sound bar over ARC due to the issue described above.
So... yeah. This stuff is really complex, unfortunately, due to all of the various combinations of technology and different limitations interacting with each other. If your sound bar has HDMI inputs itself, you might try connecting the CCwGTV directly to the sound bar. That way, it's sending 5.1 channels of uncompressed audio over the regular HDMI audio channel and the sound bar should be able to play all of that audio correctly through left, center, right, left-rear, right-rear, and low-frequency-effects channels. It would then be sending the video up to the TV via the existing HDMI connection. That's similar to what I do using my Denon receiver – all of my video sources are connected to the receiver and it then feeds just the video to my TV. But, if your soundbar doesn't have HDMI inputs, and eARC isn't an option, I'm not sure I can think of any other options right now.
Edit to add: I tried to look up the specifications for JBL Multibeam sound bars, and it looks like they do have an HDMI input. So, you can at least try that if yours is similar. If you need more than one input, you may be able to use the other inputs on your TV for other devices that don't have quite as many constraints.