Why a designer-created SKU is not in the catalog
A SKU you created as a designer stays private until a Catalog Manager approves it, so here is what approval changes.
The SKU only enters the business unit's catalog when a Catalog Manager approves an approval request for it.
Approval both adds the SKU to the business unit inventory and converts the SKU and its containing group to org ownership, after which it behaves like any other catalog item (and the creator loses their exclusive edit lock on it).
Creating a regular catalog SKU requires the Catalog Manager, Production Designer or MES Admin role at the org or in that business unit; the designer-owned creation path is the only one open to plain designers.