Hi, I am getting booted a lot because the game sound is not playing if the tab is not the active one. I am running Chrome on macOS. I have recently put all my Warzone tabs in a separate window, but that doesn't seem to fix the problem. Any ideas? It may be a chrome issue.

This won't help with the game sound, but you might try changing your account settings > notification settings. I tried having email open in a tab, and set the push notification to email immediately when it was my turn so even if the sound didn't work, I could see that I had a new email. Not really a solution, but a possible work around.

I mean. Tarnationed google search page can play sounds on inactive tabs (https://www.google.com/search?client=opera&q=google+timer&sourceid=opera&ie=UTF-8&oe=UTF-8).
Why Warzone can't?

There have been previous cases of the game advancement sounds not working. You can try disable auto discarding for your tabs on chrome://discards/, maybe that will solve your issue.

I noticed you are a WZ member, so you could use the Standalone Client to get the Windows version of the mobile app. See https://www.warzone.com/wiki/Standalone_Client for more info and the download links.