Admin Settings: edit the household timezone and auto-set it from the browser zone when unset

Adds timezone to the HouseholdSettings client type and a Timezone field
(text input with a datalist of common IANA zones) to the Preferences form.
Save validates the value as UTC or an Area/Location name and patches it
only when changed. When the loaded timezone is empty, the screen patches
the browser's Intl zone once before showing the form, so nothing the admin
enters can be overwritten; a missing or unusable zone leaves the field empty.

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

admin/src/api/settings.ts

@@ -17,6 +17,8 @@ export interface HouseholdSettings {
   afternoon_reminder_enabled: boolean;
   end_of_day_report_enabled: boolean;
   celebration_enabled: boolean;
+  /** IANA zone name (e.g. "America/New_York"); "" means the API host's local time. */
+  timezone: string;
 }
 
 /** Only the supplied fields are updated; the API answers with all of them. */