GeoSeries.extract_unique_points()
and GeoSeries.get_coordinates()
should indeed do the trick.
If you get an error that these functions don't exist, probably you are using an old version of geopandasGeoPandas. The current version is 0.14.4.
Use the following command to check the version of geopandasGeoPandas and its dependencies:
import geopandas
geopandas.show_versions()
import geopandas
print(geopandas.show_versions())