There is no finished out-of-the-box backup feature for ZHA as of yet, again see this feature request:
You could, however, do it manually or make your own scripts where script for backup/restoring Silicon Labs based dongles could be made with “bellows” and script for backup/restoring Texas Instruments based dongles could be made with “zigpy-znp” which have CLI tools to backup and restore respectively.
https://gist.github.com/EverythingSmartHome/990f2436608fd347cd20cf0009b5cef4
The video by Everything Smart Home linked above goes over the steps and commands needed.