feat(08-03): create JKSessionChatButton with unread badge

- Displays chat icon from assets
- Badge shows unread count (1-99) or "99+" for 100+
- Badge hidden when count = 0
- Reduced opacity when window already open
- Click handler opens chat window and sets active channel
- useCallback for handleClick optimization

jam-ui/src/components/client/JKSessionChatButton.js

@@ -0,0 +1,78 @@
+import React, { useCallback } from 'react';
+import { useDispatch, useSelector } from 'react-redux';
+import {
+  openChatWindow,
+  setActiveChannel,
+  selectTotalUnreadCount,
+  selectIsChatWindowOpen
+} from '../../store/features/sessionChatSlice';
+import chatIcon from '../../assets/img/client/chat.svg';
+
+const JKSessionChatButton = ({ sessionId }) => {
+  const dispatch = useDispatch();
+  const unreadCount = useSelector(selectTotalUnreadCount);
+  const isWindowOpen = useSelector(selectIsChatWindowOpen);
+
+  const handleClick = useCallback(() => {
+    if (isWindowOpen) {
+      // Window already open - do nothing (or focus window if possible)
+      return;
+    }
+
+    // Set active channel to session chat
+    dispatch(setActiveChannel({
+      channel: sessionId,
+      channelType: 'session'
+    }));
+
+    // Open chat window
+    dispatch(openChatWindow());
+  }, [dispatch, sessionId, isWindowOpen]);
+
+  // Format badge text
+  const getBadgeText = () => {
+    if (unreadCount === 0) return '';
+    if (unreadCount >= 100) return '99+';
+    return String(unreadCount);
+  };
+
+  return (
+    <div style={{ position: 'relative', display: 'inline-block' }}>
+      <img
+        src={chatIcon}
+        alt="Chat"
+        onClick={handleClick}
+        style={{
+          cursor: 'pointer',
+          width: '24px',
+          height: '24px',
+          opacity: isWindowOpen ? 0.6 : 1
+        }}
+        title="Open session chat"
+      />
+      {unreadCount > 0 && (
+        <div
+          style={{
+            position: 'absolute',
+            top: '-6px',
+            right: '-6px',
+            backgroundColor: '#dc3545', // Bootstrap danger red
+            color: 'white',
+            borderRadius: '10px',
+            padding: '2px 6px',
+            fontSize: '11px',
+            fontWeight: 'bold',
+            lineHeight: '1',
+            minWidth: '18px',
+            textAlign: 'center',
+            boxShadow: '0 1px 3px rgba(0,0,0,0.3)'
+          }}
+        >
+          {getBadgeText()}
+        </div>
+      )}
+    </div>
+  );
+};
+
+export default JKSessionChatButton;