Widget output should be saved in notebooks

[billti]

Currently, when a notebook is saved with output, the rendering of the widgets is not saved. For example, a saved notebook on GitHub appears as below, (and in VS Code it shows nothing in the cell on reopen).

It would be good if we could capture the widget state, or at least a rendering, for when displaying notebooks (or exporting to HTML).

There appears to be external issues blocking this currently. Relevant issues are:

• Widgets not displaying properly in HTML jupyter/nbconvert#923
• Feature Request: Enable ipywidget rendering after notebook restart jupyterlab/jupyterlab#15361
• Save notebook widget state vscode-jupyter#4404
• Widget output is not kept when the notebook is closed manzt/anywidget#101