The latest fabric version of CBC required 0.89.3, but Create Fabric only support 0.88.1. As the result, the latest CBC cannot work with Create on 1.20.1.

I agree, this has a problem. Because the problems associated with the fapi version Create, as well as other mods (for example, sodium, which does not work normally for version 0.5.x+ with Create (fapi 0.88.1)

Yes, that'd be really great. In the meantime, it's possible to use an older version (0.5.2)

This has been fixed in the latest indev version and will be closed on the next release.

Will address this in a later patch/minor version for CBC