fix: clients sync to server terminals instead of creating new ones

- Remove auto-creation of terminal sessions from init/selectSession/switchAgent
- Clients only connect to existing alive terminals from server registry
- Remove localStorage persistence (agent/sessionId) — state derived from server
- Refine session-state types: new AgentStatus values, LastError interface
- UI improvements: AgentBadge, ChatContainer, UserInput, BashCard updates
- Simplify claude-hook routes, update session-state service

server/services/terminal.ts

@@ -608,19 +608,25 @@ export function startTerminalServer() {
 }
 
 // Claude status types
-type ClaudeStatus = 'idle' | 'processing' | 'toolUse' | 'toolDone' | 'reading' | 'writing' | 'sessionStart' | 'subagentStart' | 'subagentStop' | 'notification' | 'permissionRequest' | 'thinking'
+type ClaudeStatus = 'idle' | 'thinking' | 'toolUse' | 'reading' | 'writing' | 'sessionStart' | 'sessionEnd' | 'permissionRequest' | 'interrupted' | 'error'
 
 // Broadcast Claude status to ALL clients across ALL sessions
 export function broadcastClaudeStatus(status: ClaudeStatus, tool?: string, agent?: string) {
   const agentName = agent || 'main'
 
-  // Track agent running state from sessionStart
+  // Track agent running state
   if (status === 'sessionStart') {
     const state = agentSessions.get(agentName)
     if (state) {
       state.isAgentRunning = true
       console.log(`[Terminal] Agent ${agentName} marked as running (sessionStart)`)
     }
+  } else if (status === 'sessionEnd') {
+    const state = agentSessions.get(agentName)
+    if (state) {
+      state.isAgentRunning = false
+      console.log(`[Terminal] Agent ${agentName} marked as stopped (sessionEnd)`)
+    }
   }
 
   const message = JSON.stringify({