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/context/ClaudeTerminalContext.tsx

@@ -0,0 +1,42 @@
+import React, { createContext, useContext, useState, ReactNode } from 'react';
+
+interface ClaudeTerminalContextType {
+  // Terminal visibility state
+  isOpen: boolean;
+  setIsOpen: (open: boolean) => void;
+  isExpanded: boolean;
+  setIsExpanded: (expanded: boolean) => void;
+
+  // Connection state (updated by the terminal component)
+  isConnected: boolean;
+  setIsConnected: (connected: boolean) => void;
+}
+
+const ClaudeTerminalContext = createContext<ClaudeTerminalContextType | undefined>(undefined);
+
+export const ClaudeTerminalProvider: React.FC<{ children: ReactNode }> = ({ children }) => {
+  const [isOpen, setIsOpen] = useState(false);
+  const [isExpanded, setIsExpanded] = useState(false);
+  const [isConnected, setIsConnected] = useState(false);
+
+  return (
+    <ClaudeTerminalContext.Provider value={{
+      isOpen,
+      setIsOpen,
+      isExpanded,
+      setIsExpanded,
+      isConnected,
+      setIsConnected
+    }}>
+      {children}
+    </ClaudeTerminalContext.Provider>
+  );
+};
+
+export const useClaudeTerminal = () => {
+  const context = useContext(ClaudeTerminalContext);
+  if (context === undefined) {
+    throw new Error('useClaudeTerminal must be used within a ClaudeTerminalProvider');
+  }
+  return context;
+};