There is a system level mute/volume control, but only when using a paired via Bluetooth audio device, or, Homepods.
I use the optical out of my tv to a DAC, that has its own Volume control.
The TV, if i press mute on its remote, it does nothing, since Optical Out (Receiver) is always on and not controlled by the TV at all.
Things may work differently if one is using a HDMI ARC/eARC audio device, like a sound bar. Though, I think HDMI CEC control is done by the TV, and not the Apple TV.?
You can also program the Apple TV remote to use IR to control audio devices, but, i do not think the actual Apple TV knows the state of IR controlled devices.
So....tldr, I too am not certain, as to how Apple is implementing this, Show Subtitles when mute, unless one is using Bluetooth / Homepods type audio.