Remove every automatic timezone-setting mechanism (task 7f685179)

The application timezone is now only ever set by an admin saving it:

- API: drop adopt_reported_timezone; the panel household clock reads the
  stored settings only and ignores any timezone request header.
- Integration: stop reporting Home Assistant's time_zone in an
  X-NestQuest-Timezone header (snapshot, completion and SSE requests).
- Admin app: remove the browser-zone detection and the automatic PATCH
  on load; the timezone field stays a manual control.
- Remove the timezone_configured marker from the core settings, the
  settings store and the admin settings API. A stored document that
  still carries the key loads harmlessly (unknown keys are ignored).

Tests replace the adoption expectations with proofs that a panel
timezone header never changes the stored settings, a fresh install's
empty zone stays empty with no settings write, the admin settings carry
no timezone_configured, and a manual admin timezone PATCH persists.

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

tests/test_coordinator.py

@@ -686,8 +686,8 @@ async def test_coordinator_configured_token_builds_real_client(
         hass, entry, session_factory=_session_factory
     )
     assert isinstance(real_client, NestQuestApiClient)
-    # Home Assistant's zone is reported to the API (task 6351b36d).
-    assert real_client._household_timezone == hass.config.time_zone
+    # Home Assistant's zone is not reported to the API (task 7f685179).
+    assert real_client._headers() == {"Authorization": "Bearer tok"}
 
     set_coordinator_client(entry, real_client)
     assert await async_setup_entry(hass, entry) is True