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For example: Does a shapefile have a geotransform?

The answer is probably: No, a vector dataset does not have a geotransform, because the purpose of a geotransform is to transform between projection coordinates and raster coordinates. But, I have not found anywhere that explicitly says that.

The documentation for GDALDataset::GetGeoTransform() ( https://gdal.org/api/gdaldataset_cpp.html ) says:

The default transform ... should be returned even when a CE_Failure error is returned, such as for formats that don’t support transformation to projection coordinates.

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GDAL has raster API and vector API. GDALDataset belongs to the raster side but you should look at the vector API at https://gdal.org/api/index.html#vector-api.

API document does not explicitly say anything about what does not exist but because vector API does not define GeoTransform you can trust that shapefiles do not have it.

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