Add timezone selector to Admin settings with full-stack support

- Add `timezone` column to User model (VARCHAR 64, default UTC) with
  idempotent startup migration
- Expose and persist timezone via PATCH /api/users/me
- Fix TimerEvent.occurred_at serialization to include UTC offset marker
  (+00:00) so JavaScript correctly parses timestamps as UTC
- Add frontend utility (src/utils/time.js) with timezone-aware
  formatTime, getHHMM, getDateInTZ, tzDateTimeToUTC helpers and a
  curated IANA timezone list
- Add Settings section to Admin page with timezone dropdown; saves to
  both the API and localStorage for the unauthenticated TV view
- Update Activity Log to display and edit times in the user's timezone
- Update TV dashboard clock to respect the saved timezone
- Update README: features, setup steps, usage table, WebSocket events

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/views/LogView.vue

@@ -81,7 +81,7 @@
 
               <!-- Display row -->
               <div v-else class="event-row" :class="entry._type">
-                <div class="event-time">{{ formatTime(entry.occurred_at) }}</div>
+                <div class="event-time">{{ fmtTime(entry.occurred_at) }}</div>
                 <div
                   class="event-dot"
                   :style="entry.subject_color ? { background: entry.subject_color } : {}"
@@ -119,11 +119,14 @@
 <script setup>
 import { ref, computed, onMounted, watch } from 'vue'
 import { useChildrenStore } from '@/stores/children'
+import { useAuthStore } from '@/stores/auth'
 import api from '@/composables/useApi'
 import NavBar from '@/components/NavBar.vue'
 import ChildSelector from '@/components/ChildSelector.vue'
+import { formatTime, getHHMM, getDateInTZ, tzDateTimeToUTC } from '@/utils/time'
 
 const childrenStore = useChildrenStore()
+const authStore = useAuthStore()
 const timeline = ref([])
 const manualLogs = ref([])
 const showForm = ref(false)
@@ -175,10 +178,8 @@ function formatDate(dateStr) {
   return d.toLocaleDateString([], { weekday: 'long', month: 'long', day: 'numeric', year: 'numeric' })
 }
 
-function formatTime(isoStr) {
-  if (!isoStr) return ''
-  const d = new Date(isoStr)
-  return d.toLocaleTimeString([], { hour: 'numeric', minute: '2-digit' })
+function fmtTime(isoStr) {
+  return formatTime(isoStr, authStore.timezone)
 }
 
 const EVENT_META = {
@@ -205,10 +206,10 @@ function eventLabel(entry) {
 function startEdit(entry) {
   editingEntry.value = entry
   if (entry._type === 'event') {
-    const d = new Date(entry.occurred_at)
-    const hh = String(d.getHours()).padStart(2, '0')
-    const mm = String(d.getMinutes()).padStart(2, '0')
-    editDraft.value = { event_type: entry.event_type, time: `${hh}:${mm}` }
+    editDraft.value = {
+      event_type: entry.event_type,
+      time: getHHMM(entry.occurred_at, authStore.timezone),
+    }
   } else {
     editDraft.value = { notes: entry.notes || '' }
   }
@@ -216,12 +217,11 @@ function startEdit(entry) {
 
 async function saveEdit(entry) {
   if (entry._type === 'event') {
-    const original = new Date(entry.occurred_at)
-    const [hh, mm] = editDraft.value.time.split(':').map(Number)
-    original.setHours(hh, mm, 0, 0)
+    const dateInTZ = getDateInTZ(entry.occurred_at, authStore.timezone)
+    const utcDate = tzDateTimeToUTC(dateInTZ, editDraft.value.time, authStore.timezone)
     await api.patch(`/api/logs/timeline/${entry.id}`, {
       event_type: editDraft.value.event_type,
-      occurred_at: original.toISOString(),
+      occurred_at: utcDate.toISOString(),
     })
   } else {
     await api.patch(`/api/logs/${entry.id}`, { notes: editDraft.value.notes })