Voicemail backup is coming to the Google Phone app in a future update according to strings of code found in the latest APK file of the app. The most recent version puts users onto version 10, and not only points towards upcoming features and improvements, but also introduces some new stuff too that should already be live for those who are on this most recent version, assuming the update has already hit your device. If it hasn't and you'd like to update, you can easily grab the version 10 APK from the button down below and sideload the APK onto your device to replace the existing version that you have installed.
As for what's officially new with this update to Google Phone, the phone app will now allow users to follow up a call with a message to the recipient that can add some context so the recipient has a better understanding as to the reason of the call. While this could certainly turn out to be a useful feature it seems to only activate in a limited capacity, as it's reported that it won't pop up if a voice call connection actually goes through. For example, if you try to make a call and you aren't able to connect due to a bad connection, then it's suggested that this is a possible situation where the Google Phone app would show you options to send a message to the person you were trying to reach. There appears to be multiple options for responses though there isn't a large list of reconfigured options. Luckily you can also write a custom message if you desire.
That's the only new feature that is currently live, but an upcoming update will include not only the voicemail backup feature, but also RCS calling. Voicemail backup will do just as it sounds, essentially. It'll let users backup voicemail messages that they have been keeping stored in their voicemail inbox. This will only really be useful if you never delete those message, but it should be nice to have in the event that you want to save one or two as well. As for the RCS calling, voice calls may get some rich calling features that allow for incoming calls to include additional data and information for the call recipient, such as images, location, and messages, though it isn't quite clear yet how those would all look if they were attached.