feat(auth): introduce backend auth module

Port RFC-001 authentication core from PR #1728:
- JWT token handling (create_access_token, decode_token, TokenPayload)
- Password hashing (bcrypt) with verify_password
- SQLite UserRepository with base interface
- Provider Factory pattern (LocalAuthProvider)
- CLI reset_admin tool
- Auth-specific errors (AuthErrorCode, TokenError, AuthErrorResponse)

Deps:
- bcrypt>=4.0.0
- pyjwt>=2.9.0
- email-validator>=2.0.0
- backend/uv.toml pins public PyPI index

Tests: 12 pure unit tests (test_auth_config.py, test_auth_errors.py).

Scope note: authz.py, test_auth.py, and test_auth_type_system.py are
deferred to commit 2 because they depend on middleware and deps wiring
that is not yet in place. Commit 1 stays "pure new files only" as the
spec mandates.

backend/app/gateway/auth/repositories/base.py

@@ -0,0 +1,82 @@
+"""User repository interface for abstracting database operations."""
+
+from abc import ABC, abstractmethod
+
+from app.gateway.auth.models import User
+
+
+class UserRepository(ABC):
+    """Abstract interface for user data storage.
+
+    Implement this interface to support different storage backends
+    (SQLite)
+    """
+
+    @abstractmethod
+    async def create_user(self, user: User) -> User:
+        """Create a new user.
+
+        Args:
+            user: User object to create
+
+        Returns:
+            Created User with ID assigned
+
+        Raises:
+            ValueError: If email already exists
+        """
+        ...
+
+    @abstractmethod
+    async def get_user_by_id(self, user_id: str) -> User | None:
+        """Get user by ID.
+
+        Args:
+            user_id: User UUID as string
+
+        Returns:
+            User if found, None otherwise
+        """
+        ...
+
+    @abstractmethod
+    async def get_user_by_email(self, email: str) -> User | None:
+        """Get user by email.
+
+        Args:
+            email: User email address
+
+        Returns:
+            User if found, None otherwise
+        """
+        ...
+
+    @abstractmethod
+    async def update_user(self, user: User) -> User:
+        """Update an existing user.
+
+        Args:
+            user: User object with updated fields
+
+        Returns:
+            Updated User
+        """
+        ...
+
+    @abstractmethod
+    async def count_users(self) -> int:
+        """Return total number of registered users."""
+        ...
+
+    @abstractmethod
+    async def get_user_by_oauth(self, provider: str, oauth_id: str) -> User | None:
+        """Get user by OAuth provider and ID.
+
+        Args:
+            provider: OAuth provider name (e.g. 'github', 'google')
+            oauth_id: User ID from the OAuth provider
+
+        Returns:
+            User if found, None otherwise
+        """
+        ...