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>

frontend/src/cards/party-board.ts

@@ -937,10 +937,12 @@ export class NestQuestPartyBoardCard extends LitElement {
     `;
   }
 
-  /** The zone the visible date and clock render in: the application
-   *  timezone the admin stored (published on the household rollup by
-   *  custom_components/nestquest/sensor.py — ``timezone``).  Only when
-   *  none is stored does Home Assistant's zone (or the browser's) apply. */
+  /** The zone the visible date and clock render in: the API's effective
+   *  application timezone — the stored zone, or the API host's when none
+   *  is stored (published on the household rollup by
+   *  custom_components/nestquest/sensor.py — ``timezone``).  Only when the
+   *  rollup carries none does Home Assistant's zone (or the browser's)
+   *  apply. */
   private _timeZone(): string | undefined {
     const stored = this._state("sensor.nestquest_household_quests_due_today")
       ?.attributes?.timezone;

frontend/src/cards/quest-log.ts

@@ -1749,10 +1749,12 @@ export class NestQuestQuestLogCard extends LitElement {
     `;
   }
 
-  /** The zone the visible date and clock render in: the application
-   *  timezone the admin stored (published on the household rollup by
-   *  custom_components/nestquest/sensor.py — ``timezone``).  Only when
-   *  none is stored does Home Assistant's zone (or the browser's) apply. */
+  /** The zone the visible date and clock render in: the API's effective
+   *  application timezone — the stored zone, or the API host's when none
+   *  is stored (published on the household rollup by
+   *  custom_components/nestquest/sensor.py — ``timezone``).  Only when the
+   *  rollup carries none does Home Assistant's zone (or the browser's)
+   *  apply. */
   private _timeZone(): string | undefined {
     const stored = this._state("sensor.nestquest_household_quests_due_today")
       ?.attributes?.timezone;