firestore CREDENTIALS Error when deploying firebase cloud function written in python

[REQUIRED] Environment info
firebase-tools:12.4.7

Platform: windows with python version of 3.11

[REQUIRED] Test case

i have code like below in for firebase cloud function in main.py.
when i test function using `firebase emulators:start --only functions` it worked perfectly

now when i try to deploy it using `firebase deploy --only functions ` it gave me below error while pointing to db = firestore.client()
line in code

error
"""""""""
raise exceptions.DefaultCredentialsError(_CLOUD_SDK_MISSING_CREDENTIALS)
google.auth.exceptions.DefaultCredentialsError: Your default credentials were not found. To set up Application Default Credentials, see https://cloud.google.com/docs/authentication/external/set-up-adc for more information.

"""""""""
code
"""
from firebase_functions import https_fn, options
import firebase_admin
from firebase_admin import firestore
app = firebase_admin.initialize_app()
options.set_global_options(timeout_sec=1000)

db = firestore.client()

### firebase function that write something to firestore database is written below
"""

[REQUIRED] Steps to reproduce

use above code in main.py inside functions folder and try to deploy functions you will get same error

[REQUIRED] Expected behavior

credential should be automatically added since i am logged into my account using firebase login and using correct Project ID. it did not ask for credential when i was tasing using `firebase emulators:start --only functions` and it was working perfectly.

[REQUIRED] Actual behavior

it's asking for credential