Calling authenticated vs public Google Cloud function from Flutter app

Question

I followed these steps to get the bearer token to successfully call an authenticated HTTP Google Cloud function from my Android Flutter app. The function processes a Braintree payment nonce. I had to include the "service_account" JSON in my project, which has private_key and private_key_id fields. This JSON is stored as an asset in my app.

I am concerned about storing this private information in my app. Would it be better to have my function public and not store this information in the app?