I don't think there's any automated way to discover which system libraries a package uses. You could find out manually by watching for errors when you try to run your image and adding any libraries that fail to load. As long as your Python dependencies aren't changing, the external dependencies should generally be unchanged also.

Oh, and did I mention, read the docs for each Python dependency, e.g. gdal:

Dependencies

• libgdal (3.11.4 or greater).