Exporting lines drawn by mouse to SVG

Take a look here:
ArrayList of objects / Examples / Processing.org

Instead of balls create an empty ArrayList of PVectors in setup().

You don’t have the co-ordinates in the PVector.

I always start simple and build on that.
Consider just storing the PVectors for now and drawing lines in a for loop.

void svgRecord() 
  PGraphics svg = createGraphics(width, height, SVG, "output.svg");
  svg.stroke(255, 0, 0);
  svg.line(0, 0, width, height);              // This works!
  for (int j = 1; j < line.size(); j++)       
    // Your line

Later you can deal with shapes or create a PShape.

Your approach with shape may very well work… it did not initially when testing.
I throttled back to simply first to get a working example to build on first

Example here of drawing lines from last point to current point:
Vertex Trail with fading alpha possible?