refactor: extract _handleInitialized method for clearer lifecycle hook

Mirrors the Go SDK pattern where the initialized notification handler
is a named method rather than an inline closure.

Author: felixweinberger

packages/server/src/server/server.ts

@@ -133,16 +133,18 @@ export class Server extends Protocol<ServerContext> {
         }
 
         this.setRequestHandler('initialize', request => this._oninitialize(request));
-        this.setNotificationHandler('notifications/initialized', () => {
-            this.startPeriodicPing();
-            this.oninitialized?.();
-        });
+        this.setNotificationHandler('notifications/initialized', () => this._handleInitialized());
 
         if (this._capabilities.logging) {
             this._registerLoggingHandler();
         }
     }
 
+    private _handleInitialized(): void {
+        this.startPeriodicPing();
+        this.oninitialized?.();
+    }
+
     private _registerLoggingHandler(): void {
         this.setRequestHandler('logging/setLevel', async (request, ctx) => {
             const transportSessionId: string | undefined =