Implement Function to Check Unique Username in Database

[Alpha17-2]

Description

We need to implement a function in our Flutter app that checks whether a username already exists in the Firebase Firestore database to ensure each username is unique. This function should query the 'user' collection and return whether the username is available or already taken.

Acceptance Criteria

• The function should accurately check the existence of a username in the Firebase Firestore database.
• The UI should display appropriate messages indicating whether the username is available or taken.
• Ensure proper error handling and user feedback.