Sound via Bluetooth shuts off during quiet
It's the "feature" of the soundbar called "Auto Standby" -- it shuts down the audio amplifier when there is no audio to play, and then it needs some time in order to turn the amplifier back on when it detects that audio has returned. Unfortunately, it does that even when connected to power source (to reduce power consumption). I've checked the manual (https://docs.sony.com/release/HTCT80_EN_ES_FR.pdf), and it seem that on your model it isn't possible to turn auto standby off.

The only workaround is to prevent the soundbar from going into standby by periodically playing sound on it, but that will be very annoying, since it must be a real sound, not silence.