I'm not sure

    <svg xmlns="http://www.w3.org/2000/svg" version="1.1">
      <image xmlns:xlink="https://www.w3.org/1999/xlink" xlink:href="data:..." width='800' height='600'/>
    </svg>

is a particularly interesting SVG image that has any benefits over the equivalent PNG.

I mean that the image should be saved in vector format! Not bitmap.

Paint is a bitmap image editor. What would you like the result to be? A <rect> for every pixel placed by the pencil tool?

The pencil tool could create a svg path.