Given the recent functionality and limited historical knowledge of branch versioning, there is seemingly very limited information available from ESRI on specifically migrating an existing SDE currently using traditional versioning to branch versioning. A dedicated technical document on this effort (or even better, an ArcGIS Pro tool to assist with this effort) is greatly needed.
There are lots of documents dedicated to enabling branch versioning in an SDE from scratch, but none that I can find specifically outlining making the conversion from traditional versioning, while preserving data in existing current archive tables, and other needed info to prevent data loss.