I am recently testing out calling the YouTube API v3 from Python (transitioning from Rust), and I initially struggled with this, as the Google Docs on the usage are not too clear.
I got tips after referencing the Quickstart Section in Python:
Here is my Python version:
$ python
Python 3.11.2
To start out with, first I ran pip install to install the following Python modules:
pip install \
    google-api-python-client~=2.85.0 \
    google-auth-oauthlib~=1.0.0 \
    google-auth-httplib2~=0.1.0
Once those dependencies are installed (in a virtual environment, preferrably) the rest is rather straightforward.
First set up an OAuth app and ensure you have a client_secret.json file to work with. Place this file in the same directory as the Python script below.
Now, you can use this script to test -- replacing VIDEO_ID with the YouTube video ID (visibility: private) under your personal channel or account.
"""
Script to retrieve info on a (Private) video in an owned YT channel.
See:
    https://developers.google.com/docs/api/quickstart/python
"""
from pathlib import Path
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
# Enter a Video ("Private" visibility) in your YT Channel, for testing purposes
VIDEO_ID = 'REPLACE-ME'
# Parent Folder of this Python Script
SCRIPT_DIR = Path(__file__).parent
# The CLIENT_SECRET_FILE variable specifies the name of a file that contains
# the OAuth 2.0 information for this application, including its client_id and
# client_secret. You can acquire an OAuth 2.0 client ID and client secret from
# the Google API Console at
# https://console.cloud.google.com/.
# Please ensure that you have enabled the YouTube Data API for your project.
# For more information about using OAuth2 to access the YouTube Data API, see:
#   https://developers.google.com/youtube/v3/guides/authentication
# For more information about the client_secrets.json file format, see:
#   https://developers.google.com/api-client-library/python/guide/aaa_client_secrets
CLIENT_SECRET_FILE = str(SCRIPT_DIR / 'client_secret.json')
# The file token.json stores the user's access and refresh tokens.
TOKEN_FILE = SCRIPT_DIR / 'token.json'
# OAuth 2.0 access scopes.
YOUTUBE_READ_ONLY_SCOPE = "https://www.googleapis.com/auth/youtube.readonly"
YOUTUBE_WRITE_SCOPE = "https://www.googleapis.com/auth/youtube.force-ssl"
SCOPES = [YOUTUBE_READ_ONLY_SCOPE, YOUTUBE_WRITE_SCOPE]
# API information
YOUTUBE_API_SERVICE_NAME = "youtube"
YOUTUBE_API_VERSION = "v3"
def main():
    # API client
    youtube = get_authenticated_service()
    # Query for an owned video
    response = youtube.videos().list(
        part="id",
        id=VIDEO_ID,
    ).execute()
    # Print the result
    print(response)
def get_authenticated_service():
    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 TOKEN_FILE.exists():
        creds = Credentials.from_authorized_user_file(str(TOKEN_FILE), SCOPES)
    # 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(
                CLIENT_SECRET_FILE,
                scopes=SCOPES,
            )
            creds = flow.run_local_server(port=0)
        # Save the credentials for the next run
        TOKEN_FILE.write_text(creds.to_json())
    return build(
        YOUTUBE_API_SERVICE_NAME,
        YOUTUBE_API_VERSION,
        credentials=creds,
    )
if __name__ == '__main__':
    main()