PC3 Phase 3.3: rate-limit the auth endpoints

app/rate_limit.py: an in-process sliding-window limiter (single-worker
backend, so no Redis needed -- flagged for if that changes). /register and
/login are capped at 10 attempts / minute / client IP (X-Forwarded-For
aware), returning 429 + Retry-After past that. Blunts credential
brute-force, which the backend had no protection against.

- conftest.py resets the limiter between tests (every TestClient request
  looks like one IP).
- tests/test_rate_limit.py: threshold, shared bucket, per-key window. 77 passed.

CORS reviewed while here: already an explicit origin allowlist
(settings.CORS_ORIGINS), not "*" -- and the Godot client isn't a browser
so it doesn't apply there anyway. Left as-is.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015jtxAiu5dAW4WxCNdGkrkJ

backend/tests/test_rate_limit.py

@@ -0,0 +1,51 @@
+"""The auth endpoints are rate-limited per client IP."""
+
+import pytest
+from fastapi.testclient import TestClient
+
+from app import rate_limit
+from app.main import app
+
+
+@pytest.fixture(autouse=True)
+def _clean_limiter():
+    # This module tests the limiter itself, so start each test from empty
+    # and don't let conftest's between-test reset interfere mid-test.
+    rate_limit.reset_all()
+    yield
+    rate_limit.reset_all()
+
+
+def test_login_is_limited_after_the_threshold():
+    client = TestClient(app)
+    codes = []
+    for i in range(15):
+        r = client.post("/api/auth/login", data={"username": f"nobody{i}", "password": "x"})
+        codes.append(r.status_code)
+    # First 10 get through to the (failing) auth check; the rest are 429.
+    assert codes[:10] == [401] * 10
+    assert 429 in codes[10:]
+    assert codes[-1] == 429
+
+
+def test_register_shares_the_same_bucket():
+    client = TestClient(app)
+    # Burn the budget on login...
+    for i in range(10):
+        client.post("/api/auth/login", data={"username": f"x{i}", "password": "y"})
+    # ...register from the same IP is now blocked too.
+    r = client.post("/api/auth/register", json={
+        "username": "rl_user", "email": "rl@e.com",
+        "password": "secret123", "date_of_birth": "1990-01-01",
+    })
+    assert r.status_code == 429
+    assert "Retry-After" in r.headers
+
+
+def test_limiter_window_is_per_key():
+    limiter = rate_limit.SlidingWindowLimiter(max_hits=2, window_seconds=60)
+    limiter.check("a")
+    limiter.check("a")
+    with pytest.raises(Exception):
+        limiter.check("a")
+    limiter.check("b")  # different key, unaffected