fix(sync): clear dead emitter and ignore IllegalStateException

dap-gateway/src/main/java/io/shinhanlife/dap/mcg/sync/CustomWebMvcSseServerTransportProvider.java

@@ -224,7 +224,8 @@ public class CustomWebMvcSseServerTransportProvider implements McpServerTranspor
                     }
                 } catch (Exception e) {
                     if (e.getClass().getSimpleName().contains("AsyncRequestNotUsableException") || 
-                        (e.getCause() != null && e.getCause() instanceof java.io.IOException)) {
+                        (e.getCause() != null && e.getCause() instanceof java.io.IOException) ||
+                        (e instanceof IllegalStateException && e.getMessage() != null && e.getMessage().contains("already completed"))) {
                         log.debug("SSE emitter is disconnected (expected in Warm Pool): {}", e.getMessage());
                     } else {
                         log.error("Error sending message to SSE emitter", e);
@@ -235,6 +236,10 @@ public class CustomWebMvcSseServerTransportProvider implements McpServerTranspor
                             this.emitter.completeWithError(e);
                         } catch (Exception ignored) {
                             // ignore already completed
+                        } finally {
+                            // 죽은 Emitter를 null로 초기화하여 다음 5초 주기 때 재시도하지 않도록 방지
+                            // 클라이언트가 재연결하면 setEmitter(새 Emitter)를 통해 덮어씌워짐
+                            this.emitter = null;
                         }
                     }
                 }