Whenever I would receive a call and the caller would leave a voicemail, I would receive an error message from the Visual Voicemail app reporting a problem had occurred and to call customer support with error code 9007. After calling and working together with a Verizon customer support technician we determined that the Visual Voicemail app exclusively uses mobile network data to operate and the issue occurs while being connected to a Wi-Fi network. Disconnecting from Wi-Fi would immediately solve the issue. Of course, this doesn't REALLY solve the issue so we dug deeper.
We may have found a solution to the larger issue (it worked in my case at least). I think an update may have broken the Visual Voicemail app's permission to use mobile data while on Wi-Fi and the permission is now hidden and/or otherwise inaccessible.
Try going into Settings > Apps and clicking the three vertical dots in the upper corner. Choose the "Reset App Preferences" option. This does nuke all the app preferences for all of your apps, but it seems to be the only way to reset the voicemail app mobile app data permission.
The only other thing you might check (I have not tested this) is whether you are using an app that manages network traffic, such as AdGuard. Make sure to either disable AdGuard from managing the voicemail app completely or at least verify the app doesn't have any settings explicitly applied that would interfere.
That's all I've got. Hope this helps anyone out there still experiencing this inconvenience.