I’d recommend using Setting Up a Project in Asana | Product Guide • Asana Product Guide which will replicate your section+tasks into a new, temporary project. In the original project, create the new section, then in the new project select all tasks and change the project membership from the new project to original project. Now drag and drop them under the new section. Finally, delete the new, temporary project. (This used to be simpler when sections were task types and you could change their project membership; not anymore.)
If you do this regularly you could also look into How to Use Asana Project Templates | Product Guide • Asana Product Guide.
Hope that helps,
Larry