ZHA integration to do nightly backup of both Zigbee Coordinator adapter/dongle/stick and Zigbee network/database?

No guarantees of that, I’m not even sure if any Home Assistant founders are using ZHA themselves(?).

FYI, zigpy developer puddly has however started development on a unified command line interface for zigpy radios so zigpy could hopfully contain all needed backup commands for any radio in the future(?).

https://github.com/zigpy/zigpy/issues/557

https://github.com/zigpy/zigpy/pull/848

https://github.com/zigpy/zigpy/issues/842

Perhaps if and when all unified backup commands are in zigpy then the “zigpy-cli” will get those as well.

https://github.com/zigpy/zigpy-cli

No it only contains bellows and zigpy-znp commands he used to do manual backup and restore, see:

https://gist.github.com/EverythingSmartHome/990f2436608fd347cd20cf0009b5cef4

https://github.com/zigpy/zigpy/wiki/Coordinator-Backup-and-Migration

https://github.com/zigpy/zigpy-znp/blob/4ac608c82b6f48d304bab9a20bd648450bed54a7/TOOLS.md#tools

https://community.home-assistant.io/t/backup-your-zha-husbzb-1-stick-and-even-seamlessly-migrate-to-a-new-stick-without-re-pairing/229044

So today you would have to write your own batch script and automate scheduling when it will run.