I don't use Super Duper, nor have I as yet (because of all the issues) updated to Catalina; but a little googling finds some info. This has a pretty good description of the differences ?in Catalina, and seems to say that a recent beta of Super Duper can mostly handle it, although for situations like an encrypted drive, some extra work by the user will likely be needed.
For those who prefer Carbon Copy Cloner, a very quick look what's happening there appears similar to me, save that perhaps it's the latest regular (non-beta) version that can handle it:
They also have a link with the background information:?
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Since upgrading to Catalina I have been unable to make a bootable clone using Super Duper, which I have used for years. Super Duper simply won¡¯t creator copy the system patrician. Time machine copies it. Is this normal?
Mackbook Air 6.2, 256 GB SSD, 4 GB, Catalina 10.15
Dick