If it works then the easiest would be to use the blueprint for zha-toolkit as then backups could be done online without stopping ZHA
https://github.com/mdeweerd/zha-toolkit
Otherwise you for now would need to stop/disable ZHA to perform offline backup via bellows directly:
https://github.com/zigpy/zigpy/wiki/Coordinator-Backup-and-Migration
https://github.com/zigpy/bellows/blob/dev/README.md#nvram-backup-and-restore
PS: Regardless consider vote to show interest → ZHA integration to do nightly backup of both Zigbee Coordinator adapter/dongle/stick and Zigbee database?