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/App.tsx

@@ -1,7 +1,9 @@
 import { BrowserRouter, Routes, Route } from 'react-router-dom';
 import { QueryClient, QueryClientProvider } from '@tanstack/react-query';
 import { StudyProvider } from './context/StudyContext';
+import { ClaudeTerminalProvider } from './context/ClaudeTerminalContext';
 import { MainLayout } from './components/layout/MainLayout';
+import { GlobalClaudeTerminal } from './components/GlobalClaudeTerminal';
 import Home from './pages/Home';
 import Dashboard from './pages/Dashboard';
 import Results from './pages/Results';
@@ -19,19 +21,24 @@ function App() {
   return (
     <QueryClientProvider client={queryClient}>
       <StudyProvider>
-        <BrowserRouter>
-          <Routes>
-            {/* Home page - no sidebar layout */}
-            <Route path="/" element={<Home />} />
+        <ClaudeTerminalProvider>
+          <BrowserRouter>
+            <Routes>
+              {/* Home page - no sidebar layout */}
+              <Route path="/" element={<Home />} />
 
-            {/* Study pages - with sidebar layout */}
-            <Route element={<MainLayout />}>
-              <Route path="dashboard" element={<Dashboard />} />
-              <Route path="results" element={<Results />} />
-              <Route path="analytics" element={<Dashboard />} />
-            </Route>
-          </Routes>
-        </BrowserRouter>
+              {/* Study pages - with sidebar layout */}
+              <Route element={<MainLayout />}>
+                <Route path="dashboard" element={<Dashboard />} />
+                <Route path="results" element={<Results />} />
+                <Route path="analytics" element={<Dashboard />} />
+              </Route>
+            </Routes>
+
+            {/* Global Claude Terminal - persists across navigation */}
+            <GlobalClaudeTerminal />
+          </BrowserRouter>
+        </ClaudeTerminalProvider>
       </StudyProvider>
     </QueryClientProvider>
   );