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>

custom_components/nestquest/core/snapshot.py

@@ -97,8 +97,9 @@ class NestQuestSnapshot:
     children: tuple[ChildDaySnapshot, ...]
     cycle_day: int
     #: The application timezone the admin stored (``""`` when unset —
-    #: the host's local time).  The panel cards format their visible
-    #: date and clock in it; it never re-resolves the day itself.
+    #: the host's local time; the API publishes its effective zone in
+    #: its place, api/host_zone.py).  The panel cards format their
+    #: visible date and clock in it; it never re-resolves the day itself.
     timezone: str = ""