Not quite - if you play Apple Music (or even Tidal) using the native Apple TV apps, then they stream directly from the cloud. (So not just the HomePod that acts this way) .And this is using the Apple TV remote, not Siri (which won't work with Tidal of course anyway).
If you ask other Airplay 2 speakers to then join in the music from the Apple TV, it is the Apple TV that shares the stream to the other speakers. So you're phone is not involved, bar the play / pause functional control.
But otherwise you are correct - if you stream to an Airplay device from your phone / tablet, then the chain is cloud - phone - speaker.
From the reports it seems as if the new TV's will act as a receiver / like an AP2 speaker only - and as such the audio from, for example broadcast / cable TV, won't be share-able to other AP2 speakers.
For that you'll need to continue using Network Link-ing - which was the most salient question that the new AP2 TV's raised, at least to me.