Persist an explicit timezone choice (timezone_configured)

The admin settings screen auto-set the browser zone whenever it loaded an
empty timezone, guarded only by a per-mount ref. After an admin cleared the
timezone (empty = API-host-local), the next open re-fetched "" and
auto-set the browser zone again, so the empty choice could not persist.

Add a twelfth settings field, timezone_configured (strict bool, default
false), carried by the core settings table, the stored JSON document and
the admin GET/PATCH. The screen now auto-sets only when the timezone is
empty AND timezone_configured is false, patching the flag with the
detected zone; saving the timezone field (including clearing it) also
sends timezone_configured: true. Detection returning nothing sets nothing.

Task: a0e7649c-58b0-4aa3-91b5-cf426e334a76 (release review TZ-001)

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

custom_components/nestquest/core/const.py

@@ -119,6 +119,12 @@ DEFAULT_AUTOMATION_ENABLED = True
 # Home Assistant's configured ``time_zone`` and ignores this field.
 CONF_TIMEZONE = "timezone"
 DEFAULT_TIMEZONE = ""
+# Whether the admin has made an explicit ``timezone`` choice.  ``False``
+# (a fresh install) lets the admin UI auto-set the browser's zone once;
+# ``True`` pins the stored value — including an explicitly-chosen empty
+# ``timezone`` (the API host's local time) — so it is never auto-set again.
+CONF_TIMEZONE_CONFIGURED = "timezone_configured"
+DEFAULT_TIMEZONE_CONFIGURED = False
 
 # Panel-plane API client (Feature 18): the integration reaches the
 # NestQuest API service (Feature 16) over HTTP instead of the database.