Using the yfiles_jupyter_graphs widget is actually a good entry point to the yFiles apps here.
For example, see the NetworkX graph-import example notebook
https://colab.research.google.com/github/yWorks/yfiles-jupyter-graphs/blob/main/examples/13_networkx_import.ipynb
The widget makes NetworkX attributes in the node's/edge's properties available. These properties may then be used in the different yfiles_jupyter_graphs mapping functions, e.g.
* node_label_mapping
* node_color_mapping
* edge_label_mapping
* edge_color_mapping (note how the above-mentioned sample notebook shows this is the very last embedding)
* etc. (see the documentation
https://yworks.github.io/yfiles-jupyter-graphs/02_graph_widget/#methods or the extensive examples
https://github.com/yWorks/yfiles-jupyter-graphs/tree/main/examples).
Once the properties are mapped in the widget's graph, you can either use the "Export to yEd Live" or "Export to Data Explorer" feature. The graph will then be sent to these applications just like it is configured in the widget.
Technically, the other NetworkX attributes are also available in the sent data, because all properties are stored in the GraphML file that is generated by the "Export to <app>" feature.
You could also export it to yEd Live and use it to download a GraphML file (Menu -> Save -> Download) that is compatible with yEd Live / yEd / Data Explorer, although the properties won't be available in yEd Live and yEd (only the Data Explorer allows some access to it afterward). Therefore, you should map them already within the yfiles_jupyter_graphs_widget to your liking.
Of course, you could also use different approaches to create a compatible file (e.g. nx.write_graphml) but you need to modify the file programmatically to make specific attributes appear in the other yFiles apps, otherwise, only the structure is read (as Thomas explained).
Tl;dr: So my recommendation is to use the yfiles_jupyter_graphs widget as a starting point, apply the data mappings as you see fit, then export it to yEd Live (or Data Explorer) from within the jupyter widget, and go from there.