Partial Solution: Download SVG to Inkscape, save as a DXF file, then you can load it into QGIS. This should at least provide you with most of the line in QGIS.
However, it will not yet be correctly linked to geographic references or style, and different layers can be in different places, because SVG has some operations of scaling and translation to parts of map data that are ignored by QGIS or Inkscape. You may need to work with the layer at a time. This is probably not a problem, because maybe you are only interested in the added data on the map, and not the base map (country outlines, etc.), since you probably want to overlay your data on a standard base layer of the map (natural land , OpenStreetMap tile).
The only way I can see the conversion at this time is to develop the affine transformation parameters and use the QgsAffine plugin, but this requires that you develop the parameters in advance by setting the known source coordinates to known target coordinates.
But do hundreds? You might be better off writing some sort of custom SVG parsing code for each ...