When Google’s Messages app gained web support in June of last year, you accessed it by visiting messages.android.com and then scanning a QR code from your phone to pair up your computer’s browser. That original address you visited is likely going to change to a google.com domain.
For some, you can already access Messages for Web by going to messages.google.com/web. It’s the same experience there that you’ve had previously, just a new domain. If it’s not working for you yet, don’t worry, Google hasn’t technically made the switch official and still links to the older android.com URL everywhere.
I’m sure Google won’t make this a big deal and will redirect users once they move it permanently. But if you want to get ahead of the game, feel free to start using it now. Again, it’s the same service, just a different URL.