Yes, muting is on the receiving side: when you mute a group (or global mute) you won't hear anyone, and they can all see that you've muted and aren't there.
The push-to-talk is on the sending side. So when you're not pushing, your mic is muted. And when you click the mute button, your speakers are muted.
Is it possible to mark yourself as away? I could see it might encourage the expectation to always be present on the receiving end.