[JoshTriplett]

You can do SMS via Android Messages and use messages.android.com on a computer. However, unlike Hangouts, it just connects to your phone to send and receive messages.

Google Fi will be unchanged; I've been using Messages from the beginning. Voice, however, has a much better experience with Hangouts than with the standalone Voice app, and in particular the standalone Voice app doesn't let you make VoIP calls as far as I can tell.

[mike00632]

What do you mean by, "However, unlike Hangouts, it just connects to your phone to send and receive messages,"? My Google Voice number is my primary number but not my cell-service number. Would messages.android.com send/receive SMS as my Google Voice number or my cellular carrier number?

[JoshTriplett]

Whichever number you have working through the Android Messages app on your phone. messages.android.com just connects (via Google) to the app on your phone, displays your messages from that, and lets you compose and send messages via that.

[int_19h]

It needs to be something that can work as a background app with notifications etc.

[JoshTriplett]

Messages on the web does support notifications, though you do have to keep it open. (But then, the same applies to Hangouts unless you use the Chrome app.)