Soundbar: Cold/Warm Shutdown?

[Peepnbrick]

So here's the story: The built-in speakers on my TV stopped working, but the audio still works on my cable box (I checked it with another TV). I bought a Vizio Soundbar so that I wouldn't have to get a whole new TV. Well, when I got it, I realized I had forgotten that the cable box stays on after the TV turns off (so that it can keep recording things), and that means that the soudbar, plugged into the cable box, will keep playing sound even after the TV is off.

 

I tried plugging the soundbar into the TV, but neither of the outputs worked, nor did changing the input on the soundbar or any of the settings on the TV, which probably means that it is not just the speakers but rather the whole sound system of the TV that's shot.

 

Luckily, I had a Surge Protector laying around that has a Switching feature: Basically, you plug the TV into the control outlet on it, and that means the other devices in the power strip mirror the activity state of the TV. While this solves the problem of the sound staying on after the TV is off, I'm worried that just cutting the power like this will hurt the soundbar, as opposed to pressing the power button and letting it shutoff cleanly.

 

So I suppose there are a couple of questions here:

1. Do Surge Protectors with this switching feature generally perform a Cold Shut Down (just cutting the power), or a warm shutdown?
   1. I can't seem to tell any difference between the Surge Protector turning it off (the supposed Cold Shutdown) or me pressing the power button (the Warm Shutdown), but I'm not sure.
2. Would this cold shutdown be harmful to the Soundbar?
3. Is there anything else I could try to get the Soundbar to work when plugged into the TV, as this would be the optimal solution?