@Atomix the Xbox360 was designed before HDMI was a thing but some models were adapted see this page https://support.xbox.com/en-GB/help/xbox-360/console/configure-audio-settings for how to set up the audio over HDMI. I would try PCM audio which is stereo but is the most likely to work.
It maybe useful to try the setting on the Glass/Connected Devices/HDMI which improves compatability with older devices.
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65inch Sky Glass, 3 Sky Streaming Pucks, Sky Ultrafast + and Sky SR213(white Wifi Max hub) main Wifi from 3 TP-Link Deco M4 units in access point mode
