You can only backup your ZST39 in Z-Wave JS UI. You can’t run both add-ons at the same time. Only one addon can have access to the controller.
To switch to Z-Wave JS UI you need to follow this guide. Switching Z-Wave JS Addons with Minimal Downtime! Z-Wave JS (Official) to Z-Wave JS UI (Community)
Once you switch over if you want to work from the integration you can continue to do so like you would with the Z-Wave JS addon
Yes your automations are getting backed up in your HA backups. You can verify this by downloading the backup and extracting it’s files.