Add Google Login to Existing Flutter App

I have an existing Flutter app and I want to integrate a new feature for Google login alongside the existing email and password login.

Key Requirements:
- Create separate buttons for Google login and email login
- Implement Google login feature
- Ensure seamless functionality with existing email login

Please note that I already have the backend services set up to support these login methods.

Post-login Display:
- After logging in with Google, the app should display the user's email address and profile picture.

Ideal Skills:
- Proficiency in Flutter
- Experience with Google login integration
- Understanding of user authentication processes
- Backend services familiarity

Please ensure a smooth, bug-free implementation for optimal user experience.