Adopt Home Assistant's time zone for the API household clock

The deployed API host runs UTC and the household `timezone` setting was
never set, so the panel snapshot read UTC: morning quests showed overdue
hours early and `today_iso` rolled over at UTC midnight.

The integration now reports `hass.config.time_zone` on every panel
request (`X-NestQuest-Timezone`).  While the admin has not chosen a zone
(`timezone_configured` is false) the API adopts and persists it, so the
panel, the admin plane, and the missed-sweep scheduler all read the
household clock out of the box.  An explicit admin choice — including an
explicitly chosen empty zone — still wins; an invalid reported zone is
logged and ignored.  No schema change.

Task: 6351b36d-0eef-4e7d-bf5a-96b754cbc883

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

api/routes_panel.py

@@ -9,8 +9,9 @@ this router inherits the check).
 The snapshot route is a thin adapter over the bundled core: it performs
 NO business logic.  It reads the live database off ``app.state.db``,
 resolves ONE timezone-aware ``now`` (the host clock re-expressed in the
-stored household ``timezone`` setting — the API host may run UTC while
-the household does not), calls the pure
+household ``timezone`` — the API host may run UTC while the household
+does not; until the admin chooses a zone it is the Home Assistant zone
+the integration reports in :data:`PANEL_TIMEZONE_HEADER`), calls the pure
 :func:`nestquest_core.snapshot.build_snapshot`, shapes each child's
 instances through :func:`nestquest_core.snapshot.instance_payload` with
 ``include_missed=False`` (D-009: missed instances are OMITTED from the
@@ -53,6 +54,7 @@ from __future__ import annotations
 
 import datetime
 import importlib
+import logging
 
 from fastapi import APIRouter, Depends, HTTPException, Request
 from fastapi.responses import StreamingResponse
@@ -62,6 +64,7 @@ from api.database import DatabaseState
 from api.dependencies import require_panel_token
 from api.nestquest_core import (
     core_completion,
+    core_const,
     core_events,
     core_settings_store,
     core_snapshot,
@@ -69,6 +72,12 @@ from api.nestquest_core import (
 from api import transitions as api_transitions
 from api.sse import transition_event_stream
 
+LOGGER = logging.getLogger(__name__)
+
+#: The request header the integration reports Home Assistant's
+#: configured IANA ``time_zone`` in.
+PANEL_TIMEZONE_HEADER = core_const.PANEL_TIMEZONE_HEADER
+
 #: The instance DAO, imported on the app's core copy for the
 #: child-mismatch guard on the complete route.
 _dao_instances = importlib.import_module("nestquest_core.dao_instances")
@@ -179,16 +188,35 @@ def _local_now() -> datetime.datetime:
 
 
 async def _household_clock(
-    database: object,
+    database: object, request: Request
 ) -> tuple[object, datetime.datetime]:
-    """Return the stored settings and ONE household-local clock read.
+    """Return the settings and ONE household-local clock read.
 
     The API host may run UTC while the household does not, so the one
-    :func:`_local_now` read is re-expressed in the stored settings'
-    ``timezone`` (:meth:`NestQuestSettings.household_now`); an unset
-    zone keeps the host's local time.
+    :func:`_local_now` read is re-expressed in the settings' ``timezone``
+    (:meth:`NestQuestSettings.household_now`).  The integration reports
+    Home Assistant's ``time_zone`` in :data:`PANEL_TIMEZONE_HEADER`;
+    until the admin chooses a zone it is adopted and persisted
+    (:func:`nestquest_core.settings_store.adopt_reported_timezone`), so
+    the scheduler and the admin plane follow it too.  An invalid
+    reported zone is logged and ignored — the panel keeps serving on
+    the stored settings.
     """
-    settings = await core_settings_store.load_settings(database)
+    reported = request.headers.get(PANEL_TIMEZONE_HEADER, "").strip()
+    if reported:
+        try:
+            settings = await core_settings_store.adopt_reported_timezone(
+                database, reported
+            )
+        except ValueError:
+            LOGGER.warning(
+                "Ignoring invalid %s header value %r",
+                PANEL_TIMEZONE_HEADER,
+                reported,
+            )
+            settings = await core_settings_store.load_settings(database)
+    else:
+        settings = await core_settings_store.load_settings(database)
     return settings, settings.household_now(_local_now())
 
 
@@ -210,7 +238,7 @@ async def panel_snapshot(request: Request) -> PanelSnapshotResponse:
     :class:`PanelSnapshotResponse`.
     """
     state: DatabaseState = request.app.state.db
-    settings, now = await _household_clock(state.database)
+    settings, now = await _household_clock(state.database, request)
     snapshot = await core_snapshot.build_snapshot(
         state.database, settings, now
     )
@@ -297,7 +325,7 @@ async def panel_complete_instance(
             detail="Quest instance not found for this child",
         )
 
-    _settings, now = await _household_clock(database)
+    _settings, now = await _household_clock(database, request)
     try:
         result = await core_completion.complete_instance(
             database,