Markaos
Indeed, try switching your smartphone to airplane mode and see how far your voice commands get you.
Did that (or rather disabled mobile data and WiFi, because airplane mode would still keep the WiFi on), and then I dictated this sentence after the parentheses. So Google’s voice input works offline just fine.
Or do they mean something like a smart assistant? In that case fair, but it’s not like it will work with text input either.
It is true, however, that Google Translate doesn’t do offline voice translation even if the language you’re trying to translate from is downloaded for system-wide voice recognition.
That indeed is a Bluetooth feature that supposedly makes audio quality better by only lowering the volume using the actual speaker driver instead of doing it digitally and potentially throwing away some quiet sounds. In theory, doing it this way is always better and should be preferred. In practice, many devices handle it terribly.
If you want to turn the feature off, you can enable developer options on your phone (settings -> About phone -> tap Build number a bunch of times) and turn off absolute volume. That will give you back software volume control with fine-grained adjustments.