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/__init__.py

@@ -0,0 +1,17 @@
+"""NestQuest API service.
+
+A standalone FastAPI deployable that owns the NestQuest database and
+exposes it over HTTP to the Home Assistant integration (panel plane) and
+the admin PWA (admin plane).  See Feature 16 (task cd03735b) in the
+project tracker for the full contract.
+
+This package imports the NestQuest domain ``core`` WITHOUT executing
+``custom_components/nestquest/__init__.py`` — that parent package's
+``__init__.py`` imports ``homeassistant``, which is absent from the
+API's runtime.  The coupling is encapsulated in
+:mod:`api.nestquest_core` (a ``sys.path`` bootstrap that makes ``core``
+importable as a top-level package).  It is a TRANSITIONAL coupling that
+Feature 18 will revisit: once the integration becomes a thin API client
+and ``core`` moves out of the integration bundle, this helper goes away.
+"""
+from __future__ import annotations