In both of those, though, I assumed that you would be selecting the data range in the Calc spreadsheet or Writer table before inserting the chart. Which you normally would be.
If you choose Insert > Chart in Calc, in the new tool, without a range selected, it's not much use. You get a big blank chart.
In Writer, however, at least in this stage of development of the tool, you get something different when you choose Insert > Object > Chart with no data range selected. Thanks to Linda from Largo for pointing this out.
You get this window where you can not only fill in the names on the X and Y axes and the data, but you can add and remove rows and columns of data, and move rows and columns around.
This is nice if you have the data written down somewhere but not in a chart or table, and it's just quicker to slam in the data manually than to base it on a chart or table. It took about twenty seconds to make this chart. (It would have taken more if I'd had any actual data on penguins and marmots as pets. ;> )
That was the chart data table, and then I just clicked the red X in the upper right corner to close and update the chart. Here's what it looks like.
This chart approach does lack titles, and X and Y axis titles. However, you can just make them with text boxes. Choose View > Toolbars > Drawing (deselect the chart first) and use the Text tool to draw a text box outside of the chart area. Type what you want in the text box, then drag it into the chart area.
In this example, I also clicked on and shrank the inner data part of the chart to leave room for the title I created with the text tool.