I think im right in saying that their are HDMI splitters you can buy which were mostly invented for people running out of HDMI inputs on the TV.
Even Argos sell them now but ive never used one. You might find the cheapers ones have a manual switch over rather than automatic.
The SKY signal to the TV goes off when the soundbar is off because the signal is not passing through without the soundbar switched on. This is quite normal and common, even on my Sony AV receiver.
If you think about it, you are using the soundbar now rather than the TV for sound right?
If the video signal passed on to the TV whilst the soundbar was off, you would have a picture on the TV but no sound.