As already mentioned, you can not backup ConBee/RaspBee with bellows as the bellows library and CLI tools is only for Silicon Labs based Zigbee dongles/adapters.
ConBee/RaspBee uses " deconz" as radio type in ZHA which is dependent on the zigpy-deconz project.
I am however not sure if zigpy-deconz support ConBee/RaspBee backup to zigpy’s “Open ZigBee Coordinator Backup Format” (universal backup and restore format needed for cross-hardware migrations) as of yet but you can try asking about that in https://github.com/zigpy/open-coordinator-backup/issues or https://github.com/zigpy/zigpy/discussions (as if it does not then either waiting until zigpy-deconz does add support for it or re-pairing all devices is your only choices currently).
If there is no support as of yet there might be in the future as believe the zigpy developers have plans to also support ConBee/RaspBee though zigpy-deconz (though understand that the zigpy developers are volunteers working on it for free as a hobby).
Which exact dongle model do you have? ITead sells two different models that do not use the same chip.
“SONOFF Zigbee 3.0 USB Dongle Plus” has Texas Instruments chip so use “znp” radio type in ZHA.
“Zigbee 3.0 USB Dongle” has a Silabs chip so uses “ezsp” radio type (dependent on bellows) in ZHA.
And again, ConBee/RaspBee uses “deconz” (dependent on the zigpy-deconz project) in ZHA.