Selecting audio device output to cast on Remote Play (Speakers or Headphones): only Speakers is working

[Asmkv]

I have Speakers on my computer. I can start to remote play any game with sound playing on them, and on the TV, so they can hear what I'm hearing on the PC.
But I play some games with headphones (like Hellblade for a better spatial effect).

And I can't play the sound on TV if it comes from my headphones (HyperX Cloud Alpha Wireless).
In the Windows volume mixer, as soon as I switch my output device on this game for the headphones, I hear the sound from it, but there is no sound on TV. As soon as I come back to the speakers, the sound is back on the TV and on the speakers.

I tried many things: disabling Steam Streaming Spearks, enabling it back, switching my default output device between the speakers and the headphones, switching the output device from the windows volume mixer.
I lowered the quality of the sound from the headphones too, setting it from 24 bits to 16 bits into the device properties.
I tried with the Steam beta version too.

Any help on it please ? Why Steam can only cast sound from the speakers ?

[Asmkv]

Ok, it was the last thing I didnt try: I had to disabled my speakers, set my headphones as default output device. Reboot Windows, restart Steam and the game is both on my headphones and the TV.