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/config.py

@@ -0,0 +1,61 @@
+"""Configuration for the NestQuest API service.
+
+The API reads its single configuration knob — the SQLite database path —
+from the ``NESTQUEST_DB_PATH`` environment variable, with a documented
+default inside the OS temp directory.  This mirrors the integration's
+"explicit settings object" discipline (Feature 15's
+``core.settings``): the API never reads HA config; callers pass the
+resolved path into the database wiring.
+"""
+from __future__ import annotations
+
+import os
+import tempfile
+from dataclasses import dataclass
+from pathlib import Path
+
+#: Environment variable holding the SQLite file path.  The API opens
+#: this file on startup (creating it if absent) and applies migrations.
+DB_PATH_ENV = "NESTQUEST_DB_PATH"
+
+#: The default database location when the env var is unset.  Lives in
+#: the OS temp directory so a dev run without configuration does not
+#: litter the repo, and so tests that forget to set the env var still
+#: get a hermetic-ish path.  Production deployments ALWAYS set
+#: ``NESTQUEST_DB_PATH`` to a persistent volume path.
+_DEFAULT_DB_NAME = "nestquest.db"
+
+
+def _default_db_path() -> str:
+    return str(Path(tempfile.gettempdir()) / _DEFAULT_DB_NAME)
+
+
+@dataclass(frozen=True)
+class ApiConfig:
+    """Resolved API configuration.
+
+    Currently a single field — the SQLite path — but kept as a dataclass
+    so later tasks (auth, SSE, settings persistence) can extend it
+    without touching the call sites that read ``db_path``.
+    """
+
+    db_path: str
+
+    @classmethod
+    def from_env(cls, env: dict[str, str] | None = None) -> "ApiConfig":
+        """Build configuration from the process environment.
+
+        ``env`` defaults to ``os.environ``; tests pass an explicit dict
+        so they are hermetic (no monkeypatch of the global environ).
+        """
+        source = env if env is not None else os.environ
+        raw = source.get(DB_PATH_ENV, "").strip()
+        return cls(db_path=raw if raw else _default_db_path())
+
+
+def resolve_db_path(env: dict[str, str] | None = None) -> str:
+    """Return the resolved SQLite path (env override or documented default)."""
+    return ApiConfig.from_env(env).db_path
+
+
+__all__ = ["ApiConfig", "DB_PATH_ENV", "resolve_db_path"]