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>

admin/src/api/settings.ts

@@ -19,12 +19,6 @@ export interface HouseholdSettings {
   celebration_enabled: boolean;
   /** IANA zone name (e.g. "America/New_York"); "" means the API host's local time. */
   timezone: string;
-  /**
-   * True once the admin explicitly chose `timezone` (even ""); false on a
-   * fresh install, where the screen auto-sets the browser's zone. API-only:
-   * never shown in the form.
-   */
-  timezone_configured: boolean;
 }
 
 /** Only the supplied fields are updated; the API answers with all of them. */