Consolidate chat timeline events + auto-end inactive sessions

Timeline consolidation:
- Replace multiple LIVE_CHAT_STARTED/ENDED events with single LIVE_CHAT_SUMMARY
- Show total duration accumulated across all sessions
- Display session count (e.g., "23min 15s total - 3 sessoes")
- Show "Ativo" badge when session is active

Auto-end inactive chat sessions:
- Add cron job running every minute to check inactive sessions
- Automatically end sessions after 5 minutes of client inactivity
- Mark auto-ended sessions with "(encerrado por inatividade)" flag

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

convex/liveChat.ts

@@ -692,6 +692,67 @@ export const getTicketChatHistory = query({
   },
 })
 
+// ============================================
+// ENCERRAMENTO AUTOMATICO POR INATIVIDADE
+// ============================================
+
+// Timeout de inatividade: 5 minutos
+const INACTIVITY_TIMEOUT_MS = 5 * 60 * 1000
+
+// Mutation interna para encerrar sessoes inativas (chamada pelo cron)
+export const autoEndInactiveSessions = mutation({
+  args: {},
+  handler: async (ctx) => {
+    const now = Date.now()
+    const cutoffTime = now - INACTIVITY_TIMEOUT_MS
+
+    // Buscar todas as sessoes ativas com inatividade > 5 minutos
+    const inactiveSessions = await ctx.db
+      .query("liveChatSessions")
+      .filter((q) =>
+        q.and(
+          q.eq(q.field("status"), "ACTIVE"),
+          q.lt(q.field("lastActivityAt"), cutoffTime)
+        )
+      )
+      .collect()
+
+    let endedCount = 0
+
+    for (const session of inactiveSessions) {
+      // Encerrar a sessao
+      await ctx.db.patch(session._id, {
+        status: "ENDED",
+        endedAt: now,
+      })
+
+      // Calcular duracao da sessao
+      const durationMs = now - session.startedAt
+
+      // Registrar evento na timeline
+      await ctx.db.insert("ticketEvents", {
+        ticketId: session.ticketId,
+        type: "LIVE_CHAT_ENDED",
+        payload: {
+          sessionId: session._id,
+          agentId: session.agentId,
+          agentName: session.agentSnapshot?.name ?? "Sistema",
+          durationMs,
+          startedAt: session.startedAt,
+          endedAt: now,
+          autoEnded: true, // Flag para indicar encerramento automatico
+          reason: "inatividade",
+        },
+        createdAt: now,
+      })
+
+      endedCount++
+    }
+
+    return { endedCount }
+  },
+})
+
 // ============================================
 // UPLOAD DE ARQUIVOS (Maquina/Cliente)
 // ============================================