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/errors.py

@@ -0,0 +1,44 @@
+"""Typed error definitions for auth module.
+
+AuthErrorCode: exhaustive enum of all auth failure conditions.
+TokenError: exhaustive enum of JWT decode failures.
+AuthErrorResponse: structured error payload for HTTP responses.
+"""
+
+from enum import StrEnum
+
+from pydantic import BaseModel
+
+
+class AuthErrorCode(StrEnum):
+    """Exhaustive list of auth error conditions."""
+
+    INVALID_CREDENTIALS = "invalid_credentials"
+    TOKEN_EXPIRED = "token_expired"
+    TOKEN_INVALID = "token_invalid"
+    USER_NOT_FOUND = "user_not_found"
+    EMAIL_ALREADY_EXISTS = "email_already_exists"
+    PROVIDER_NOT_FOUND = "provider_not_found"
+    NOT_AUTHENTICATED = "not_authenticated"
+
+
+class TokenError(StrEnum):
+    """Exhaustive list of JWT decode failure reasons."""
+
+    EXPIRED = "expired"
+    INVALID_SIGNATURE = "invalid_signature"
+    MALFORMED = "malformed"
+
+
+class AuthErrorResponse(BaseModel):
+    """Structured error response — replaces bare `detail` strings."""
+
+    code: AuthErrorCode
+    message: str
+
+
+def token_error_to_code(err: TokenError) -> AuthErrorCode:
+    """Map TokenError to AuthErrorCode — single source of truth."""
+    if err == TokenError.EXPIRED:
+        return AuthErrorCode.TOKEN_EXPIRED
+    return AuthErrorCode.TOKEN_INVALID