I can't authorize gmail api application in google colaboratory

There is something wrong with the way you are loading the run_local_server if you are getting a 404 error.

The code below is my standard QuickStart for People api. I just tested it and it works fine. I am not getting a 404 error.

#   To install the Google client library for Python, run the following command:
#   pip install --upgrade google-api-python-client google-auth-httplib2 google-auth-oauthlib


from __future__ import print_function

import os.path

import google.auth.exceptions
from google.auth.transport.requests import Request
from google.oauth2.credentials import Credentials
from google_auth_oauthlib.flow import InstalledAppFlow
from googleapiclient.discovery import build
from googleapiclient.errors import HttpError

# If modifying these scopes, delete the file token.json.
SCOPES = ['https://www.googleapis.com/auth/contacts']

def main():

    """Shows basic usage of the People API.
    Prints a list of user contacts.
    """
    creds = None
    # The file token.json stores the user's access and refresh tokens, and is
    # created automatically when the authorization flow completes for the first
    # time.
    if os.path.exists('token.json'):
        try:
            creds = Credentials.from_authorized_user_file('token.json', SCOPES)
            creds.refresh(Request())
        except google.auth.exceptions.RefreshError as error:
            # if refresh token fails, reset creds to none.
            creds = None
            print(f'An error occurred: {error}')
    # If there are no (valid) credentials available, let the user log in.
    if not creds or not creds.valid:
        if creds and creds.expired and creds.refresh_token:
            creds.refresh(Request())
        else:
            flow = InstalledAppFlow.from_client_secrets_file(
                'C:YouTubedevcredentials.json', SCOPES)
            creds = flow.run_local_server(port=0)
        # Save the credentials for the next run
        with open('token.json', 'w') as token:
            token.write(creds.to_json())

    try:
        service = build('people', 'v1', credentials=creds)

        # Call the People API
        print('List 10 connection names')
        results = service.people().connections().list(
            resourceName='people/me',
            pageSize=10,
            personFields='names,emailAddresses').execute()
        connections = results.get('connections', [])

        for person in connections:
            names = person.get('names', [])
            if names:
                name = names[0].get('displayName')
                print(name)
    except HttpError as err:
        print(err)


if __name__ == '__main__':
    main()