"""Parse a base URL and return (host, port) as strings.

This function is designed to be more robust than simple string splitting, supporting various URL schemes and shapes, including those with trailing paths. It uses `urlparse` to extract the hostname and port from the base URL. If the hostname is not present, it defaults to "127.0.0.1". If the port is not present, it returns an empty string.

Args:
    base_url (str): The base URL to parse.

Returns:
    tuple[str, str]: A tuple containing the host and port as strings. The host defaults to "127.0.0.1" if not found, and the port is an empty string if not found.
"""
You should write code starting with:
from urllib.parse import urlparse

def _parse_url(base_url: str) -> tuple[str, str]:
    # TODO: Implement this function
    pass

