I investigated the issue. output_notebook() does not work fine in Quarto.
What happens is that when there are only python cells in a Quarto notebook, it is rendered with Jupyter. And output_notebook() works with Jupyter. Alas, when there are mixed R and Python cells, R is used for rendering thourgh the reticulate package. And then it does not work.
The behaviour obtained is super weird, by the way, and I describe it here : calling output_notebook() removes all pre-existing imports and variables.