feat(tui): show router inference metrics beside router lines

apps/tui-go/internal/protocol/golden_test.go

@@ -88,6 +88,17 @@ func TestDecodeGoldenServerFrames(t *testing.T) {
 				}
 			},
 		},
+		{
+			name:      "chat.turn carries router metrics",
+			json:      `{"type":"chat.turn","sessionId":"s1","turnId":"t9","role":"ROUTER","content":"hi","latencyMs":3000,"totalTokens":943,"sequence":7,"sessionSequence":2}`,
+			wantType:  TypeChatTurn,
+			eventBear: true,
+			check: func(t *testing.T, m ServerMessage) {
+				if m.LatencyMs == nil || *m.LatencyMs != 3000 || m.TotalTokens == nil || *m.TotalTokens != 943 {
+					t.Fatalf("chat.turn metrics: %+v", m)
+				}
+			},
+		},
 		{
 			name:      "snapshot_complete (non-event control frame)",
 			json:      `{"type":"snapshot_complete"}`,

apps/tui-go/internal/protocol/protocol.go

@@ -87,6 +87,10 @@ type ServerMessage struct {
 	Models  []string `json:"models"`
 	Current string   `json:"current"`
 
+	// chat.turn router metrics (nil when not a ROUTER turn or server omits them)
+	LatencyMs   *int64 `json:"latencyMs"`
+	TotalTokens *int   `json:"totalTokens"`
+
 	// resource.status (nil = unavailable)
 	GpuMemoryUsedMb   *int64 `json:"gpuMemoryUsedMb"`
 	GpuMemoryTotalMb  *int64 `json:"gpuMemoryTotalMb"`