feat(api): stats endpoint for gethomepage widget (closes #131)

Adds GET /api/v1/stats/summary, gated by HOMEPAGE_API_KEY env var and
X-API-Key header (hmac.compare_digest, matches the liveview pattern).

Payload:
  nodes / online / offline / unknown
  pending_devices (status='pending')
  zigbee_devices  (Node.ieee_address IS NOT NULL)
  last_scan_at    (max ScanRun.finished_at)

Disabled by default — endpoint returns 403 unless HOMEPAGE_API_KEY is set.
README documents activation and ships a ready-to-paste gethomepage
`customapi` widget snippet.

Tests cover: disabled-by-default, missing header, wrong key, empty DB,
and full aggregation across nodes/pending/zigbee/scan-runs.

backend/tests/test_stats.py

@@ -0,0 +1,100 @@
+"""API tests for /api/v1/stats/* (gethomepage widget)."""
+
+from __future__ import annotations
+
+from datetime import datetime, timezone
+
+import pytest
+from httpx import AsyncClient
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from app.core.config import settings
+from app.db.models import Node, PendingDevice, ScanRun
+
+
+@pytest.fixture(autouse=True)
+def _reset_homepage_key():
+    original = settings.homepage_api_key
+    settings.homepage_api_key = ""
+    yield
+    settings.homepage_api_key = original
+
+
+@pytest.mark.asyncio
+async def test_summary_disabled_when_key_unset(client: AsyncClient) -> None:
+    res = await client.get("/api/v1/stats/summary")
+    assert res.status_code == 403
+    assert "disabled" in res.json()["detail"].lower()
+
+
+@pytest.mark.asyncio
+async def test_summary_rejects_missing_header(client: AsyncClient) -> None:
+    settings.homepage_api_key = "topsecret"
+    res = await client.get("/api/v1/stats/summary")
+    assert res.status_code == 403
+
+
+@pytest.mark.asyncio
+async def test_summary_rejects_wrong_key(client: AsyncClient) -> None:
+    settings.homepage_api_key = "topsecret"
+    res = await client.get(
+        "/api/v1/stats/summary", headers={"X-API-Key": "wrong"}
+    )
+    assert res.status_code == 403
+
+
+@pytest.mark.asyncio
+async def test_summary_empty_db(client: AsyncClient) -> None:
+    settings.homepage_api_key = "topsecret"
+    res = await client.get(
+        "/api/v1/stats/summary", headers={"X-API-Key": "topsecret"}
+    )
+    assert res.status_code == 200
+    body = res.json()
+    assert body == {
+        "nodes": 0,
+        "online": 0,
+        "offline": 0,
+        "unknown": 0,
+        "pending_devices": 0,
+        "zigbee_devices": 0,
+        "last_scan_at": None,
+    }
+
+
+@pytest.mark.asyncio
+async def test_summary_aggregates_counts(
+    client: AsyncClient, db_session: AsyncSession
+) -> None:
+    settings.homepage_api_key = "topsecret"
+    finished = datetime(2026, 5, 14, 10, 0, tzinfo=timezone.utc)
+    db_session.add_all([
+        Node(type="server", label="A", status="online"),
+        Node(type="server", label="B", status="online"),
+        Node(type="server", label="C", status="offline"),
+        Node(type="server", label="D", status="unknown"),
+        Node(type="iot",    label="Z1", status="online", ieee_address="0x1"),
+        Node(type="iot",    label="Z2", status="online", ieee_address="0x2"),
+        PendingDevice(ip="10.0.0.1", status="pending"),
+        PendingDevice(ip="10.0.0.2", status="pending"),
+        PendingDevice(ip="10.0.0.3", status="hidden"),  # excluded
+        ScanRun(status="success", finished_at=finished),
+        ScanRun(status="success",
+                finished_at=datetime(2026, 5, 13, 10, 0, tzinfo=timezone.utc)),
+    ])
+    await db_session.commit()
+
+    res = await client.get(
+        "/api/v1/stats/summary", headers={"X-API-Key": "topsecret"}
+    )
+    assert res.status_code == 200
+    body = res.json()
+    assert body["nodes"] == 6
+    assert body["online"] == 4
+    assert body["offline"] == 1
+    assert body["unknown"] == 1
+    assert body["pending_devices"] == 2
+    assert body["zigbee_devices"] == 2
+    # SQLite returns naive datetimes; compare prefix only.
+    assert body["last_scan_at"] is not None
+    assert body["last_scan_at"].startswith("2026-05-14T10:00:00")