The DEATH STRANDING soundtrack is its own entry in Steam, and is only visible if you have Soundtracks selected in your Library. You can confirm this by using the small dropdown menu and ensuring that the Soundtracks box has a checkmark next to it:
You will now be able to see and install the soundtrack in your Library and listen to the music in the window that appears on the right side of your Steam app:
The soundtrack is available as MP3s on your local drive to listen to in your favorite music player!