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>

tests/test_api_household_clock.py

@@ -236,6 +236,25 @@ def test_from_options_reads_and_resiliently_defaults_timezone() -> None:
     )
 
 
+def test_settings_timezone_configured_defaults_false_and_is_strict() -> None:
+    assert _settings.NestQuestSettings().timezone_configured is False
+    assert _settings.NestQuestSettings.from_options({}).timezone_configured is False
+    assert (
+        _settings.NestQuestSettings.from_options(
+            {"timezone_configured": True}
+        ).timezone_configured
+        is True
+    )
+    for value in ("true", 1, None):
+        with pytest.raises(ValueError, match="timezone_configured"):
+            _settings.NestQuestSettings(timezone_configured=value)
+        if value is not None:
+            with pytest.raises(ValueError):
+                _settings.NestQuestSettings.from_options(
+                    {"timezone_configured": value}
+                )
+
+
 # --- the missed-sweep scheduler ----------------------------------------------