I've been using Hangouts for years, and have had my Google Voice SMS going there for years. Today they split that so I won't get my SMSes in Google Hangouts anymore.
Then, I check out Google Chat, they're idea of a replacement. Not there either. They're Chat page lets you use one chat per tab. (Not multiple windows on that page.)
Google Voice, which is how I have to get my texts now, it seems, also lets you see one thing per page. Leaving that tab open is going to mess up my phone calls, isn't it.