This may help pin down where the issue is happening…
The source of your TV video is the device that should be sending the “keep awake” signal if the TV is looking for one, for less smart TVs, they’re just looking for a signal from the video connection. If one is there, the TV will stay awake.
Sonos Arc is being sent the audio over HDMI and playing it, though Arc can send a video display if the TV is set to be playing that input, it’s just a splash screen.
If this only happens from the cable TV, the “keep awake” may need to come from that device, but it’s most likely within the TV’s sleep settings, as suggested. This page may have the right settings to check on: https://www.sony.co.uk/electronics/support/articles/00091584