Partial Solution: load SVG into Inkscape, Save as DXF file, then you can load this into QGIS. This should at least get you most of the linework into QGIS.
However, it won't yet be properly georeferenced or styled, and different layers may be in different places because the SVG has some scaling and translating operators on parts of the map data that QGIS or Inkscape is ignoring. You'll probably need to work with a layer at a time. This probably isn't a problem since maybe you are only interested in the added data on the map, and not the base map (country outlines etc) since you will probably want to overlay your data onto standard map base layer (natural earth, OpenStreetMap tiles).
The only way I see to do the transformation at present is to work out the affine transformation parameters and use the QgsAffine plugin, but that does require you to work out the parameters beforehand by fitting known source coordinates to known target coordinates.
But to do hundreds? You might be better off writing some custom SVG parsing code for each one...