How can I reproduce a manual NCBI search with Biopython Entrez module?
This can be done by using the "Search details" as a search term in Entrez.esearch:

import os
OPJ = os.path.join
base_dir = os.getcwd()

from Bio import Entrez
Entrez.email = "my_email_here"
query = "ANOS1[gene name] AND refseq[filter]"
handle = Entrez.esearch(term=query, db="nuccore", retmax=400)
ids = Entrez.read(handle)["IdList"]
with open(OPJ(base_dir, "ANOS1_orthologs_max400_ids.txt"), "w") as ids_file:
    ids_file.write("\n".join(ids))
    ids_file.write("\n")