Hi EugenSecara,
Thanks for posting here in the Google Nest Community. I’m assuming that you’re using a Chromecast with Google TV since the older versions of Chromecast have no means of pairing with Bluetooth devices and won’t be able to split the video and sound. Using the Chromecast Voice remote, you just navigate to Settings > Remotes and Accessories > Pair a remote or accessory. Once paired, you'll be able to play your apps (Netflix, Disney+, YouTube, Spotify, etc.) and see the video on the TV screen while the sound goes to the paired audio device (a Bluetooth speaker, headset, earbuds, etc.).
Please be reminded that not all devices can be paired. It all boils down to compatibility since Chromecast with Google TV uses Bluetooth 4.2, as you can see here: Chromecast specifications.
I hope this answers your question. Let us know if you still have other concerns.
Cheers,
Kimy
