Add CodeNomad-inspired two-level tab system (Phase 2)

Phase 2 of enhancement plan:
- Created project-manager.js for project-level organization
- Created session-tabs.js for session-level organization
- Created project-tabs.css with responsive design
- Added tab structure to index.html
- Cache bust: v1769083200000

Features:
- Project tabs organize sessions by working directory
- Session tabs show all sessions within active project
- Context menu for rename/duplicate/delete/close
- Visual indicators for active/running sessions
- Responsive design for mobile

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

public/claude-ide/index.html

@@ -233,7 +233,7 @@
     <script>
     (function() {
         'use strict';
-        const EXPECTED_JS_VERSION = '1769083100000';  // Cache bust for tool rendering system
+        const EXPECTED_JS_VERSION = '1769083200000';  // Cache bust for CodeNomad-inspired two-level tabs
         const CACHE_BUST_KEY = '_claude_cache_bust';
 
         // Check if we need to force reload
@@ -301,6 +301,7 @@
     <link rel="stylesheet" href="/claude/claude-ide/components/session-picker.css?v=1769027229">
     <link rel="stylesheet" href="/claude/claude-ide/components/approval-card.css?v=1769027229">
     <link rel="stylesheet" href="/claude/claude-ide/tool-rendering.css?v1769083100000">
+    <link rel="stylesheet" href="/claude/claude-ide/project-tabs.css?v1769083200000">
     <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.9.0/styles/github-dark.min.css">
 
     <!-- Monaco Editor (VS Code Editor) - AMD Loader -->
@@ -411,6 +412,16 @@
 
         <!-- Chat View -->
         <div id="chat-view" class="view">
+            <!-- Two-Level Tab System (CodeNomad-inspired) -->
+            <div id="project-tabs">
+                <!-- Project tabs rendered by project-manager.js -->
+                <div class="loading">Loading projects...</div>
+            </div>
+            <div id="session-tabs">
+                <!-- Session tabs rendered by session-tabs.js -->
+                <div class="loading">Loading sessions...</div>
+            </div>
+
             <div class="chat-layout">
                 <div class="chat-sidebar-overlay" id="chat-sidebar-overlay"></div>
                 <div class="chat-sidebar" id="chat-sidebar">
@@ -647,6 +658,8 @@
     <script src="/claude/claude-ide/preview-manager.js?v1769082165881"></script>
     <script src="/claude/claude-ide/chat-enhanced.js?v1769082165881"></script>
     <script src="/claude/claude-ide/tool-renderers.js?v1769083100000"></script>
+    <script src="/claude/claude-ide/project-manager.js?v1769083200000"></script>
+    <script src="/claude/claude-ide/session-tabs.js?v1769083200000"></script>
     <script src="/claude/claude-ide/terminal.js?v1769082165881"></script>
     <script src="/claude/claude-ide/components/monaco-editor.js?v1769082165881"></script>
     <script src="/claude/claude-ide/components/enhanced-chat-input.js?v1769082165881"></script>