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/jwt.py

@@ -0,0 +1,55 @@
+"""JWT token creation and verification."""
+
+from datetime import UTC, datetime, timedelta
+
+import jwt
+from pydantic import BaseModel
+
+from app.gateway.auth.config import get_auth_config
+from app.gateway.auth.errors import TokenError
+
+
+class TokenPayload(BaseModel):
+    """JWT token payload."""
+
+    sub: str  # user_id
+    exp: datetime
+    iat: datetime | None = None
+    ver: int = 0  # token_version — must match User.token_version
+
+
+def create_access_token(user_id: str, expires_delta: timedelta | None = None, token_version: int = 0) -> str:
+    """Create a JWT access token.
+
+    Args:
+        user_id: The user's UUID as string
+        expires_delta: Optional custom expiry, defaults to 7 days
+        token_version: User's current token_version for invalidation
+
+    Returns:
+        Encoded JWT string
+    """
+    config = get_auth_config()
+    expiry = expires_delta or timedelta(days=config.token_expiry_days)
+
+    now = datetime.now(UTC)
+    payload = {"sub": user_id, "exp": now + expiry, "iat": now, "ver": token_version}
+    return jwt.encode(payload, config.jwt_secret, algorithm="HS256")
+
+
+def decode_token(token: str) -> TokenPayload | TokenError:
+    """Decode and validate a JWT token.
+
+    Returns:
+        TokenPayload if valid, or a specific TokenError variant.
+    """
+    config = get_auth_config()
+    try:
+        payload = jwt.decode(token, config.jwt_secret, algorithms=["HS256"])
+        return TokenPayload(**payload)
+    except jwt.ExpiredSignatureError:
+        return TokenError.EXPIRED
+    except jwt.InvalidSignatureError:
+        return TokenError.INVALID_SIGNATURE
+    except jwt.PyJWTError:
+        return TokenError.MALFORMED