Hi, Boodean.
Welcome to the Apple Support Communities. We’re glad you decided to reach out about using your AirPods with your TV and soundbar. It sounds like you’re able to pair the AirPods to your TV without issue, but you’re not getting any sound out of them when you do.
We did some preliminary research on the Sony support site. It looks like you may need to check your TV configurations for audio output. These articles may help:
Your TV may not be capable of hosting both connections. If you’re not able to get it to work through reviewing the Sony support articles, we would reach out to them directly for help.
Contact Us - Electronics Support | Sony USA
Good luck!