feat: Add session management and global Claude terminal

Phase 1 - Accurate study status detection:
- Add is_optimization_running() to check for active processes
- Add get_accurate_study_status() with proper status logic
- Status now: not_started, running, paused, completed
- Add "paused" status styling (orange) to Home page

Phase 2 - Global Claude terminal:
- Create ClaudeTerminalContext for app-level state
- Create GlobalClaudeTerminal floating component
- Terminal persists across page navigation
- Shows green indicator when connected
- Remove inline terminal from Dashboard

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

atomizer-dashboard/frontend/src/pages/Home.tsx

@@ -3,6 +3,7 @@ import { useNavigate } from 'react-router-dom';
 import {
   FolderOpen,
   Play,
+  Pause,
   CheckCircle,
   Clock,
   AlertCircle,
@@ -64,6 +65,8 @@ const Home: React.FC = () => {
     switch (status) {
       case 'running':
         return <Play className="w-3.5 h-3.5" />;
+      case 'paused':
+        return <Pause className="w-3.5 h-3.5" />;
       case 'completed':
         return <CheckCircle className="w-3.5 h-3.5" />;
       case 'not_started':
@@ -81,6 +84,12 @@ const Home: React.FC = () => {
           card: 'border-green-500/30 hover:border-green-500/50',
           glow: 'shadow-green-500/10'
         };
+      case 'paused':
+        return {
+          badge: 'bg-orange-500/20 text-orange-400 border-orange-500/30',
+          card: 'border-orange-500/30 hover:border-orange-500/50',
+          glow: 'shadow-orange-500/10'
+        };
       case 'completed':
         return {
           badge: 'bg-blue-500/20 text-blue-400 border-blue-500/30',