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/database.py

@@ -0,0 +1,82 @@
+"""Database wiring for the NestQuest API service.
+
+The API owns the database (it is the writer of record per Feature 16's
+contract).  This module owns one application-lifetime
+:class:`core.db.NestQuestDatabase`: it opens the SQLite file at the
+configured path on startup, applies migrations (creating the schema on
+a fresh file), and closes the connection on shutdown.
+
+The executor callable passed into ``NestQuestDatabase`` mirrors the
+contract of ``hass.async_add_executor_job``: schedule a synchronous
+callable on a worker and await its result.  HA's own version lives on
+the event loop; the API is not HA, so it uses
+:func:`asyncio.to_thread` for the same effect — sqlite3 calls run on a
+worker thread and only plain data returns to the event loop.
+"""
+from __future__ import annotations
+
+import asyncio
+import logging
+from typing import Any
+
+from api.nestquest_core import core_db, core_migrations
+
+LOGGER = logging.getLogger(__name__)
+
+#: The async SQLite wrapper.  Re-exported so route handlers and later
+#: tasks reach it through the API package, not the bundled core.
+NestQuestDatabase = core_db.NestQuestDatabase
+
+#: The migration runner.  Re-exported for the same reason.
+apply_migrations = core_migrations.apply_migrations
+
+
+async def _executor(fn: Any, *args: Any, **kwargs: Any) -> Any:
+    """Run a synchronous callable on a worker thread and await its result.
+
+    Mirrors the contract of ``hass.async_add_executor_job`` so the
+    bundled ``NestQuestDatabase`` (written against that contract) works
+    unchanged in the API process: sqlite3 calls never block the event
+    loop, and only plain Python data (row tuples,
+    :class:`core.db.ExecutionResult`) crosses back.
+    """
+    return await asyncio.to_thread(fn, *args, **kwargs)
+
+
+class DatabaseState:
+    """Holds the live database wrapper and its resolved path.
+
+    A small container so the lifespan and the route handlers share one
+    authoritative reference; FastAPI's lifespan stores one of these on
+    ``app.state.db`` and the health route reads it back.
+    """
+
+    __slots__ = ("database", "db_path")
+
+    def __init__(self, database: NestQuestDatabase, db_path: str) -> None:
+        self.database = database
+        self.db_path = db_path
+
+    async def open_and_migrate(self) -> None:
+        """Open the connection and apply migrations to the latest version."""
+        LOGGER.info("Opening NestQuest database at %s", self.db_path)
+        await self.database.open(self.db_path)
+        version = await apply_migrations(self.database)
+        LOGGER.info("NestQuest schema at version %d", version)
+
+    async def close(self) -> None:
+        """Close the connection; safe to call even if open failed."""
+        await self.database.close()
+
+
+def make_database(db_path: str) -> DatabaseState:
+    """Construct a :class:`DatabaseState` for the given path (not yet open)."""
+    return DatabaseState(NestQuestDatabase(_executor), db_path)
+
+
+__all__ = [
+    "DatabaseState",
+    "NestQuestDatabase",
+    "apply_migrations",
+    "make_database",
+]