MartinZoller - The enablement of Unified Labeling from Azure Information Protection blade is a one time action. The backend actions are described in the blog. From that point, both services (AIP and SCC) use the same label database and therefor, there is no option to "copy labels again" as they are connected.
In Unified Labeling you need to distinguish between Policy advanced settings to Label advanced settings which have different concept then how they are configured in AIP labels. therefor, if a new label is created in AIP, you should add it's relevant advanced configuration using SCC PS.
We do recommend to manage your labels at one place after the migration, beside the scanner use case, there is no other reason to use both portals for label and policy management.