feat(chat): vincula timer automaticamente com inicio/fim do chat ao vivo

- Ao iniciar chat: inicia timer EXTERNAL automaticamente se nao houver sessao ativa
- Ao encerrar chat: pausa timer automaticamente se houver sessao ativa
- Adiciona razao de pausa END_LIVE_CHAT para identificar pausas automaticas

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

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

convex/liveChat.ts

@@ -168,7 +168,40 @@ export const startSession = mutation({
       createdAt: now,
     })
 
-    return { sessionId, isNew: true }
+    // Iniciar timer automaticamente se nao houver sessao de trabalho ativa
+    // O chat ao vivo eh considerado trabalho EXTERNAL (interacao com cliente)
+    let workSessionId: Id<"ticketWorkSessions"> | null = null
+    if (!ticket.activeSessionId && ticket.assigneeId) {
+      workSessionId = await ctx.db.insert("ticketWorkSessions", {
+        ticketId,
+        agentId: ticket.assigneeId,
+        workType: "EXTERNAL",
+        startedAt: now,
+      })
+
+      await ctx.db.patch(ticketId, {
+        working: true,
+        activeSessionId: workSessionId,
+        status: "AWAITING_ATTENDANCE",
+        updatedAt: now,
+      })
+
+      await ctx.db.insert("ticketEvents", {
+        ticketId,
+        type: "WORK_STARTED",
+        payload: {
+          actorId,
+          actorName: agent.name,
+          actorAvatar: agent.avatarUrl,
+          sessionId: workSessionId,
+          workType: "EXTERNAL",
+          source: "live_chat_auto",
+        },
+        createdAt: now,
+      })
+    }
+
+    return { sessionId, isNew: true, workSessionStarted: workSessionId !== null }
   },
 })
 
@@ -225,7 +258,60 @@ export const endSession = mutation({
       createdAt: now,
     })
 
-    return { ok: true }
+    // Pausar timer automaticamente se houver sessao de trabalho ativa
+    let workSessionPaused = false
+    const ticket = await ctx.db.get(session.ticketId)
+    if (ticket?.activeSessionId) {
+      const workSession = await ctx.db.get(ticket.activeSessionId)
+      if (workSession && !workSession.stoppedAt) {
+        const workDurationMs = now - workSession.startedAt
+        const sessionType = (workSession.workType ?? "INTERNAL").toUpperCase()
+        const deltaInternal = sessionType === "INTERNAL" ? workDurationMs : 0
+        const deltaExternal = sessionType === "EXTERNAL" ? workDurationMs : 0
+
+        // Encerrar sessao de trabalho
+        await ctx.db.patch(ticket.activeSessionId, {
+          stoppedAt: now,
+          durationMs: workDurationMs,
+          pauseReason: "END_LIVE_CHAT",
+          pauseNote: "Pausa automática ao encerrar chat ao vivo",
+        })
+
+        // Atualizar ticket
+        await ctx.db.patch(session.ticketId, {
+          working: false,
+          activeSessionId: undefined,
+          status: "PAUSED",
+          totalWorkedMs: (ticket.totalWorkedMs ?? 0) + workDurationMs,
+          internalWorkedMs: (ticket.internalWorkedMs ?? 0) + deltaInternal,
+          externalWorkedMs: (ticket.externalWorkedMs ?? 0) + deltaExternal,
+          updatedAt: now,
+        })
+
+        // Registrar evento de pausa
+        await ctx.db.insert("ticketEvents", {
+          ticketId: session.ticketId,
+          type: "WORK_PAUSED",
+          payload: {
+            actorId,
+            actorName: actor.name,
+            actorAvatar: actor.avatarUrl,
+            sessionId: workSession._id,
+            sessionDurationMs: workDurationMs,
+            workType: sessionType,
+            pauseReason: "END_LIVE_CHAT",
+            pauseReasonLabel: "Chat ao vivo encerrado",
+            pauseNote: "Pausa automática ao encerrar chat ao vivo",
+            source: "live_chat_auto",
+          },
+          createdAt: now,
+        })
+
+        workSessionPaused = true
+      }
+    }
+
+    return { ok: true, workSessionPaused }
   },
 })