Apple TV 4K gen 2 should play music from iPhone 13 Pro, while te TV is off

1. Some manufacturers have soundbars that are AirPlay-enabled. That could work as you intend to, without the need for other equipment to power up, when streaming music from your iPhone.
2. HDMI-CEC would try to power up all HDMI devices from the first device (Apple TV box), so by disabling HDMI-CEC the other devices could stay in standby. You would obviously also lose other handy CEC features if CEC is off on all devices. You’ll have to experiment with CEC off on just the TV.

szymon1982 wrote:

My setup is Apple TV 4K gen. 2 -> sound bar -> 4K Samsung TV; All this is done via HDMI

Status:

Samsung 4K TV: Off

Apple TV 4K gen 2: On

Sony soundbar: Standby

Now I would like to from my iPhone stream music to Apple TV so that the music will be played via the Sony Soundbar, but the TV need to be OFF, at the moment the TV is automatically turn on.

In basic words, I would like to listen to music, with the Samsung TV off.

[...]

This is what screen saver settings are for :-).

As @Urquhart1244 pointed out, you could disable HDMI CEC on your Samsung TV (Samsung refers to this standard as "Anynet+"), but this would minimally prevent the Apple TV Remote or the Sony Soundbar from turning the TV on and off when watching TV and may interfere with other controls (like Volume) too.

I happen to have a similar configuration: ATV4K > Sony Soundbar (HT-Z9F) > LG TV. The Sony doesn't do AirPlay, but I can play music from my iPhone direct to the Sony via Google ChromeCast over WiFi (this is app-dependent on iOS) or via Bluetooth. In either case, the Sony wants to wake up the TV to display info about the music that's currently playing. This is actually fine with me, but I prefer seeing the Apple TV's AirPlay representation of music metadata and album art on-screen (since I listen to stations that mix new music with the familiar).

So, my [Settings > General > Screen Saver] are set to start after just 2 minutes and "Show During Music and Podcasts" = No.