Ok, I just wanted to make sure this was the only question you had asked --
You may have had 2 questions on the same model, but it isn't showing up in the list of questions you have asked.
Connection H -- That's the only audio output on your TV set. Connect your soundbar to that connection.
Then go into your Tools menu, select the Sound settings, switch your speaker setting to Audio System to turn on the Audio Output (H)
Now, IF you have any SCART or component connected devices....try those FIRST, then try the HDMI next, but only IF the HDMI doesn't deliver sound to your BOSE.
Now the reason I state that is because the older RCA Audio outputs....the HDMI audio was never delivered to that type of connector. Since I don't see BOTH connectors (optical and RCA audio OUTPUTS on this TV), I can only assume that Sony was licensed to deliver BOTH types of audio to the RCA outputs.
The KEY is the Licensing. Everything has slowly migrated from RCA to Optical, and then ALL inputs moved to ONE AUDIO OUTPUT.
That's part of the Key issue....knowing when you set your TV's speaker setting to "Audio System" -- Do both HDMI and Scart/Component deliver to that output, or does only Half of the connectors do it?
Get that connected to the RCA audio outs (H) set your TV's Speaker setting to "Audio System" then try the HDMI, and then the Scart/Component inputs.
2007 was one of those years where they were transistioning to One output for all. But like I said, it was a slow process over 3-4 years.
Let me know the results you get with HDMI and Analog - Scart/Component, ok?