Inserting points in an existing line/arrow in calc

Using LibreOffice 25.8.1.1 on Win11 home edition.

When I make a line or arrow with the “Insert Line” tool or the “Lines and Arrows” tool, I get a line without any corners in it. I could make a line with one or more corners by using the “Curves and Polygons” tool, too. But I can’t seem to change the number of corners in a line afterward. All I seem to be able to do is draw a new line, painstakingly apply the styling of the old line to it one property at a time, reposition it to match the position of the old line, and then delete the old line.

This is very destructive to my workflow when I’m using line shapes in my spreadsheets since it often means spending upwards of 30 seconds just to add or remove a point if I’ve made a mistake or need to edit it after the fact. Is there a way (e.g. with Point Edit Mode) to add new points to a line without having to redo all my previous work?

In your definition, are corners the same as points?
Does there have to be a specific number of points?
What exactly is the goal?
Describe the goal as precisely as possible, not the path.