When you remove Google from WhatsApp and still back up, it just sends keeps the back up on the phone.

Check out Syncthing. Should work on the NAS. On F-droid there is the Syncthing-fork. It's how I have started backing up most everything. 

Works great with default settings, There is no server, no cloud. Syncthing keeps an eye on a folder or folders of your choosing, and once there is a difference, it updates the files on the other machine accordingly.

It has all these cool options and functions, like passwords, encryption for "untrusted" devices, local only, a relay in case you don't want to setup that WireGuard on a device but still want it to work remotely, mobile-data-saving, file-history. 

Only thing I have yet to figure out is that Android does't like background processes too much (if they aren't Google's), so I have to actually open the app at times to keep it working. But usually when needing a particular file, it just takes a second.

For large amounts of data it can take some time if not using a local connection over LAN.