This is the latest Apollo Cloud app from the app store.
As you can see it works with Ventura.
Note that the app version is 2.1.906.1, not 2.1.13. There are also versions for iOS, Windows and android, there are many management options.
We even removed the Apollo Cloud drive, formatted it and started over.
Formatted it? This may be your problem. The proper way to start over is to reset the Apollo from the app then reclaim it.
It still says that the network backup disk could not be accessed (even though it mounts the drive and it lets me login to it.
The Apollo provides network storage that time machine can use as bacup storage. If the network drive can be mounted, then the Apollo is doing it's job. I just tested my Apollo and can access the storage from both Ventura and Windows.
And in fact time machine succesfully runs on Ventura with the Apollo as storage.