Not compatible with IPython.display.set_matplotlib_formats

Normally, you can use the following lines of code, to force Jupyter to store an additional pdf version of each plot in the notebook json.
```
from IPython.display import set_matplotlib_formats
set_matplotlib_formats('png', 'pdf')
```

However, when calling `%matplotlib widget` before, only the png version of the image ist stored

Start by reproducing the interaction between `%matplotlib widget` and `IPython.display.set_matplotlib_formats('png', 'pdf')`, then inspect how the widget integration serializes figures into notebook JSON. Done means a widget-backed plot preserves both the PNG and PDF representations when those formats are requested.

Written by the indexing model from the issue text.