Enable Identity-Aware Proxy in your project. Secure function access using its permissions.

Create a service account with the Cloud Functions Viewer role. Use that service account to invoke the function.

Create a service account with the Cloud Functions Invoker role. Use that service account to invoke the function.

Create an OAuth 2.0 client ID for your calling service in the same project as the function you want to secure. Use those credentials to invoke the function.