I also want to use my existing stereo system. Roku support had a page "How to set up your Roku Streambar SE or Roku Streambar with a Roku TV system" that had the following section:
When streaming your favorite entertainment, you will only hear sound coming from your Streambar. You will not hear any sound on the speakers built-in to your TV or an existing audio system.
That makes it seem that the Streambar strips off the audio from the HDMI signal going to my TV. But that page said it was specifically for Roku TV.
What is weird to me is that for the first couple of days that I had the Streambar set up, I DID get audio through the HDMI to my TV and on to my stereo. I even experienced the "out of sync" issue that was also described on the page. So, if I had the stereo and the Streambar both producing audio, there was an "echo". My solution for that was muting the Streambar and just accepting the milliseconds mismatch between the sound and the action.
I was hoping someone from Roku support would have responded to this thread with some definitive information.