FastAPI skeleton: health, OpenAPI, core wiring (task 042dfc5c)

Add api/ with a FastAPI app that imports the bundled NestQuest core
(Feature 15) WITHOUT importing homeassistant: api/nestquest_core.py
bootstraps the integration directory onto sys.path and imports core as
a top-level package, so custom_components/nestquest/__init__.py (which
imports HA) never executes. This transitional coupling is encapsulated
in one documented helper to revisit in Feature 18.

The app reads NESTQUEST_DB_PATH (env var, documented temp default),
opens+migrates the SQLite database in a FastAPI lifespan, and serves
GET /health (200, status ok + resolved db_path) and the OpenAPI doc at
/docs and /openapi.json. Tests start the app with httpx against the
ASGI app and assert all three; a subprocess test proves the app
imports core without importing homeassistant or registering
custom_components.

Add fastapi, uvicorn, httpx to the dev dependency group; uv lock.

Suite green at 1581 (1576 baseline + 5 new API tests).

api/app.py

@@ -0,0 +1,92 @@
+"""The NestQuest FastAPI application.
+
+This module builds the ASGI app for the NestQuest API service (Feature
+16).  The skeleton here wires the bundled ``core`` (Feature 15) and
+exposes the two endpoints every later task depends on:
+
+- ``GET /health`` — returns ``200`` with a JSON status body carrying
+  ``status: "ok"`` and the resolved database path, proving the app
+  imported core, opened the database, and applied migrations.
+- ``GET /docs`` — FastAPI's auto-served OpenAPI document (Swagger UI);
+  ``/openapi.json`` is the raw schema.  No extra wiring is needed;
+  FastAPI serves both by default.
+
+The database is opened and migrated in a FastAPI lifespan context so a
+startup failure (e.g. an unwritable path) surfaces as a startup error
+rather than the first request.  The connection is closed on shutdown.
+"""
+from __future__ import annotations
+
+import logging
+from contextlib import asynccontextmanager
+from collections.abc import AsyncIterator
+
+from fastapi import FastAPI
+
+from api.config import ApiConfig
+from api.database import DatabaseState, make_database
+
+LOGGER = logging.getLogger(__name__)
+
+
+def _build_lifespan(db_path: str):
+    """Return a lifespan that opens+migrates then closes one database.
+
+    Captured as a closure so the app factory can hand the configured
+    path in without threading it through FastAPI's lifespan signature.
+    """
+
+    @asynccontextmanager
+    async def lifespan(app: FastAPI) -> AsyncIterator[None]:
+        state = make_database(db_path)
+        app.state.db = state
+        try:
+            await state.open_and_migrate()
+            yield
+        finally:
+            await state.close()
+
+    return lifespan
+
+
+def create_app(config: ApiConfig | None = None) -> FastAPI:
+    """Build the NestQuest API FastAPI app.
+
+    ``config`` defaults to one built from the process environment, so
+    ``uvicorn api.app:app`` picks up ``NESTQUEST_DB_PATH``.  Tests pass an
+    explicit config (or set the env var) so each test gets a hermetic
+    temp SQLite file.
+    """
+    cfg = config if config is not None else ApiConfig.from_env()
+
+    app = FastAPI(
+        title="NestQuest API",
+        description=(
+            "Standalone HTTP service that owns the NestQuest database and "
+            "exposes it to the Home Assistant integration (panel plane) and "
+            "the admin PWA (admin plane)."
+        ),
+        version="0.1.0",
+        lifespan=_build_lifespan(cfg.db_path),
+    )
+
+    @app.get("/health", summary="Service health")
+    async def health() -> dict[str, str]:
+        """Return service health and the resolved database path.
+
+        The body carries ``status: "ok"`` and the ``db_path`` the app
+        opened against — so a probe can confirm the app wired core and
+        reached the configured SQLite file.  Returns 200 once the
+        lifespan has opened and migrated the database.
+        """
+        state: DatabaseState = app.state.db
+        return {"status": "ok", "db_path": state.db_path}
+
+    return app
+
+
+#: The module-level app instance, for ``uvicorn api.app:app``.
+app: FastAPI = create_app()
+
+
+__all__ = ["app", "create_app"]