The new branches use the fabric MOB_CONVERSION event to copy entity data to the new entity.
The 1.20 branch does not make use of that event. As a result, when a mob converts it loses its CCA data in the process.

It would be nice having that for the 1.20 branch, too.

Could be nice, but some of the changes associated with this feature are breaking changes, so those couldn't be backported. Additionally I don't have much time to spend on backports, but if you or someone else submitted a PR with a backward-compatible version of this change I could release it.