One of the worst problems we can face in the case of update our Mac to the new operating system at the time of launch is that the applications are incompatible or have bugs with the new system.
In this case the popular Carbon Copy Cloner software, which is used for disk and partition backups in macOS alerts users to possible compatibility issues with macOS Big Sur. This means that at the time of updating the Mac it is possible that it stops working due to the new security system implemented by Apple in Big Sur and that is related to the computer's disk utility.
The software works but needs more time
Many developers warn of possible bugs with new versions, but others do not. In this case the latest version of Carbon Copy Cloner which is 5.1.22 works on macOS Big Sur, but it is only capable of creating copies of the system volume other than the boot one. The developers of this software have submitted the problem or bug directly to the Cupertino company and are working on it to fix this bug.
In this case the developers of this app They have warned of the failure but there are many others who do not usually do so, so it is always recommended before installing a new version on our Mac that all the important software for our day to day is compatible. This can be done sending an email directly to the developer or consulted the description thereof.
Many times it is better to wait a few days before installing the new operating system on the Mac, iPhone, iPad, etc, in this way we prevent this type of problem if we really need this software to work.