Publish the API's effective timezone and tolerate an older snapshot payload

TZ-002: with no zone stored the API reads its clock in the host's local
time, but the panel fell back to Home Assistant's zone and the admin app
to the browser's, so dates could disagree near midnight. The API now
names the zone it actually uses (api/host_zone.py: the stored zone, else
the host's own IANA zone from TZ, /etc/localtime or /etc/timezone) and
publishes it as the panel snapshot's `timezone` and the admin settings'
read-only `effective_timezone`. Both cards and the admin app format in
that one zone; Home Assistant's or the browser's zone applies only when
none is published.

TZ-003: snapshot_from_api_payload reads `timezone` with a "" default, so
an integration upgraded ahead of its API keeps refreshing against the
pre-change payload.

Task 7e173881-fb99-426f-a2f0-2678439ffc39

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

admin/src/api/settings.ts

@@ -19,10 +19,15 @@ export interface HouseholdSettings {
   celebration_enabled: boolean;
   /** IANA zone name (e.g. "America/New_York"); "" means the API host's local time. */
   timezone: string;
+  /**
+   * Read-only: the zone the API reads its clock in — `timezone`, or the API
+   * host's own zone when that is "" ("" only when the host's zone has no name).
+   */
+  effective_timezone: string;
 }
 
 /** Only the supplied fields are updated; the API answers with all of them. */
-export type SettingsChanges = Partial<HouseholdSettings>;
+export type SettingsChanges = Partial<Omit<HouseholdSettings, "effective_timezone">>;
 
 export const SETTINGS_PATH = "/api/v1/admin/settings";