feat(07-03): implement localStorage utilities for lastReadAt

- Add saveLastReadAt: saves timestamp with merge support
- Add loadLastReadAt: loads all timestamps with parse error handling
- Add clearLastReadAt: clears specific channel or all channels
- All functions handle localStorage errors gracefully (quota, parse errors)
- Storage key: 'jk_chat_lastReadAt'
- All 8 tests passing (GREEN phase)

Part of Phase 7 Plan 3 (WebSocket Integration & Selectors)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

jam-ui/src/helpers/chatStorage.js

@@ -0,0 +1,71 @@
+/**
+ * localStorage utilities for chat lastReadAt persistence
+ *
+ * Stores lastReadAt timestamps for each chat channel to track unread status
+ * across browser sessions. Data is stored as JSON object keyed by channel ID.
+ */
+
+const STORAGE_KEY = 'jk_chat_lastReadAt';
+
+/**
+ * Save lastReadAt timestamp for a channel
+ *
+ * Merges with existing data to preserve timestamps for other channels.
+ * Handles localStorage quota errors gracefully.
+ *
+ * @param {string} channel - Channel ID (session ID, lesson ID, or 'global')
+ * @param {string} timestamp - ISO timestamp (e.g., '2026-01-26T12:00:00Z')
+ */
+export const saveLastReadAt = (channel, timestamp) => {
+  try {
+    const existing = loadLastReadAt();
+    existing[channel] = timestamp;
+    localStorage.setItem(STORAGE_KEY, JSON.stringify(existing));
+  } catch (error) {
+    console.error('Failed to save lastReadAt:', error);
+  }
+};
+
+/**
+ * Load all lastReadAt timestamps from localStorage
+ *
+ * Returns empty object if no data exists or if JSON parsing fails.
+ *
+ * @returns {Object} Map of channel IDs to ISO timestamp strings
+ */
+export const loadLastReadAt = () => {
+  try {
+    const stored = localStorage.getItem(STORAGE_KEY);
+    if (!stored) return {};
+    return JSON.parse(stored);
+  } catch (error) {
+    console.error('Failed to load lastReadAt:', error);
+    return {};
+  }
+};
+
+/**
+ * Clear lastReadAt timestamp for a channel, or all channels
+ *
+ * If channel is specified, removes only that channel's timestamp.
+ * If no channel is specified, removes entire storage key.
+ *
+ * @param {string} [channel] - Channel ID to clear, or undefined to clear all
+ */
+export const clearLastReadAt = (channel) => {
+  try {
+    if (channel) {
+      const existing = loadLastReadAt();
+      delete existing[channel];
+      if (Object.keys(existing).length === 0) {
+        localStorage.removeItem(STORAGE_KEY);
+      } else {
+        localStorage.setItem(STORAGE_KEY, JSON.stringify(existing));
+      }
+    } else {
+      localStorage.removeItem(STORAGE_KEY);
+    }
+  } catch (error) {
+    console.error('Failed to clear lastReadAt:', error);
+  }
+};