yEd does not offer the possibility to import custom properties into existing diagrams. Nor does it offer the possibility to adopt property values from label texts.
Off the top of my head I can think of the following solutions:
You create a single custom property for edges and manually enter the label text as the property value for each edge.
You save your diagram as GraphML and create a custom script or short program that enhances the GraphML by converting your edge label texts into custom edge property values in the GraphML file. Then re-open the modified GraphML file in yEd.
You create a spreadsheet file for your diagram and use yEd's Excel import to create a diagram with custom properties.
Unfortunately, all of the above solutions require quite a lot of work.