feat(07-03): integrate localStorage with Redux slice

- Import saveLastReadAt and loadLastReadAt utilities
- Load lastReadAt from localStorage on Redux store initialization
- Save to localStorage when openChatWindow action is dispatched
- Save to localStorage when markAsRead action is dispatched
- All 68 Redux tests still passing after integration
- All 8 localStorage tests passing

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

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

jam-ui/src/store/features/sessionChatSlice.js

@@ -1,5 +1,6 @@
 import { createSlice, createAsyncThunk } from '@reduxjs/toolkit';
 import { getChatMessages, sendChatMessage } from '../../helpers/rest';
+import { saveLastReadAt, loadLastReadAt } from '../../helpers/chatStorage';
 
 /**
  * Async thunk to fetch chat history for a channel
@@ -63,7 +64,7 @@ const initialState = {
   activeChannel: null,
   channelType: null,
   unreadCounts: {},
-  lastReadAt: {},
+  lastReadAt: loadLastReadAt(), // Load from localStorage on init
   fetchStatus: {},
   fetchError: {},
   sendStatus: 'idle',
@@ -150,15 +151,17 @@ const sessionChatSlice = createSlice({
 
     /**
      * Open chat window
-     * Resets unread count for active channel
+     * Resets unread count for active channel and persists to localStorage
      */
     openChatWindow: (state) => {
       state.isWindowOpen = true;
 
       // Reset unread count for active channel
       if (state.activeChannel) {
+        const now = new Date().toISOString();
         state.unreadCounts[state.activeChannel] = 0;
-        state.lastReadAt[state.activeChannel] = new Date().toISOString();
+        state.lastReadAt[state.activeChannel] = now;
+        saveLastReadAt(state.activeChannel, now); // Persist to localStorage
       }
     },
 
@@ -172,12 +175,14 @@ const sessionChatSlice = createSlice({
 
     /**
      * Mark channel as read
-     * Resets unread count and updates lastReadAt timestamp
+     * Resets unread count, updates lastReadAt timestamp, and persists to localStorage
      */
     markAsRead: (state, action) => {
       const { channel } = action.payload;
+      const now = new Date().toISOString();
       state.unreadCounts[channel] = 0;
-      state.lastReadAt[channel] = new Date().toISOString();
+      state.lastReadAt[channel] = now;
+      saveLastReadAt(channel, now); // Persist to localStorage
     },
 
     /**