I receive the same error on Julia 1.6. It is fixed for me on Julia 1.8, so I would suggest, if possible, to update to the latest Julia version. To test it out, I recommend running the following code:
import Pkg; Pkg.add("PyCall")
using PyCall
geopandas = pyimport_conda("geopandas", "geopandas")
path_to_data = geopandas.datasets.get_path("nybb")
gdf = geopandas.read_file(path_to_data)
If it works correctly, you should see “ERROR 1: PROJ: proj_create_from_database: Open of /root/.julia/conda/3/x86_64/share/proj failed”, which appears to be the expected output based on the “Getting Started” section from the docs.