Does messages.android.com store messages on its servers?

Question

Google

Is it possible to view your SMS through a browser, does messages.android.com store messages on its servers or does it only have access when the phone is connected to the network?
The very principle of the site is similar to the web vatsap and works only if the phone is connected to the network, having authorized itself before that. And in general, what is the principle of operation of such a site - is it done for confidentiality that access is available only when a device is connected to the Internet?
Thank you.