I've been down this road before. CCC Release 6 does create bootable external drives, because that is what I do. My Mac Mini has an internal HD that is not able to run Catalina or above hardly at all (due to APFS), so I installed Catalina to one external drive and CCC'ed it to another external drive (I have two) and I let my internal HD stay with El Capitan. That way I can always boot off my internal HD to obtain a running system that I can use to build a newer system (although I've never actually HAD to do this, but it seems like a good idea - belt and suspenders, you know).
R6 is not a free upgrade unless you purchased R5 within a year before R6 was introduced (which allowed me to squeak through at no cost). I've used CCC and SuperDuper - both can create bootable external drives - after using both, I prefer CCC.
By the way, if you have the means to do so, make your primary bootable external drive an SSD - you won't believe the difference.
I created a 1TB SSD bootable drive, and it is usable. I had to not clone my music, photos, & movies to fit. I also created a 2TB bootable disk drive and it is too slow.
I contacted CCC and was told that it can't be made bootable since Apple changed something with Catalina. Well, I made bootable drives before I paid for it, and after I found a review that said it made bootable drives. But I can't upgrade my MacOS in my 1TB drive. I keep trying and it doesn't upgrade. CCC said it is not a viable solution anymore.
My own personal needs do not see any reason to clone drives as just backups. Time Machine does that. The reason I bought it was so that I could boot to an external drive. (I had a program I need fail with a MacOS upgrade and it took me several weeks to resolve that problem. I wish I had been able to run it from my backup boot drive).
I asked Mike Bombich (CCC) if I could erase my drive and then run CCC to recreate it and his reply was:
"One option to consider would be to create a "legacy bootable copy" of the system onto an external device (freshly formatted, the name isn't relevant), then boot from that device and test out your software updates there. If the software update doesn't break anything, then you can boot from the internal startup disk and apply the update there."
I think that means yes, so I'll try it.