How to specify standard GCP when using Apps Script API to create project?

Question

I would like to mimic the functionality under "Switch to a different standard Cloud project" here using the Apps Script API in Python. When I create a Script Project using the API it gets created such that it uses a Default Cloud Project and from the API documentation it's unclear how to change that.

SCRIPT_CODE = '''
function myFunction() {
# OMITTED -- this contains the actual code that the script runs
}
'''.strip()

MANIFEST = '''
{
  "timeZone": "America/New_York",
  "exceptionLogging": "CLOUD",
  "executionApi": {
    "access": "MYSELF"
  },
  
}
'''.strip()


# Authenticate using OAuth 2.0
# AUTHENTICATION CODE OMITTED

service = build('script', 'v1', credentials=creds)

# Create a new project using the Apps Script API
request = {'title': 'My Script Project'}
response = service.projects().create(body=request).execute()

script_id = response['scriptId']

# Upload two files to the project
request = {
    'files': [{
        'name': 'Test generate script from python',
        'type': 'SERVER_JS',
        'source': SCRIPT_CODE
    }, {
        'name': 'appsscript',
        'type': 'JSON',
        'source': MANIFEST
    }]
}
response = service.projects().updateContent(
    body=request,
    scriptId=script_id).execute()

# Create a new version using the Apps Script API
request = {'scriptId': script_id}
response = service.projects().versions().create(scriptId = script_id, body = request).execute()

version_number = response['versionNumber']

# Create a new deployment using the Apps Script API
request = {
    "description": f"Deployment of script {script_id}",
    "scriptId": script_id,
    "versionNumber": version_number
}
response = service.projects().deployments().create(scriptId = script_id, body = request).execute()
print(json.dumps(response, indent=2))
deployment_id = response["deploymentId"]

# Run the script using the Apps Script API
request = {
    "function": "myFunction"
}

I end up getting the below error, I believe because the authentication is with a Standard Google Cloud Project but the Apps Script Project uses a Default Google Cloud Project on creation.