The volume controls on the software remote (side buttons on the iPhone or iPad) can work for select AV receivers that support CEC Volume Controls. TVs don’t seems to support that through CEC. (Not sure about HDMI soundbars.)
The volume controls on the software remote can work for select AirPlay or Bluetooth speakers that do not have their own volume controls.
The Mute button on the software remote works for devices that support the Mute command over HDMI-CEC from the Apple TV box (or AirPlay or Bluetooth if those do not have their own volume control). The icon always has the slash. If the icon is grayed out as inactive, then the Mute command is not detected as supported by the audio system this way.
The volume control signals go from the software remote go from mobile over Wi-Fi to the Apple TV box to the audio system. There is obviously no support for IR volume control signals with mobile, which would be supported by the physical Siri Remote.