implements the notifications/initialized method

- According to
  https://modelcontextprotocol.io/specification/2025-06-18/basic/lifecycle,
  "After successful initialization, the client MUST send an initialized
  notification to indicate it is ready to begin normal operations".

lib/mcp/server.rb

@@ -74,6 +74,7 @@ module MCP
         Methods::PROMPTS_GET => method(:get_prompt),
         Methods::INITIALIZE => method(:init),
         Methods::PING => ->(_) { {} },
+        Methods::NOTIFICATIONS_INITIALIZED => ->(_) {},
 
         # No op handlers for currently unsupported methods
         Methods::RESOURCES_SUBSCRIBE => ->(_) {},

test/mcp/server_test.rb

@@ -160,6 +160,26 @@ module MCP
       assert_instrumentation_data({ method: "unsupported_method" })
     end
 
+    test "#handle notifications/initialized returns nil response" do
+      request = {
+        jsonrpc: "2.0",
+        method: "notifications/initialized",
+      }
+
+      assert_nil @server.handle(request)
+      assert_instrumentation_data({ method: "notifications/initialized" })
+    end
+
+    test "#handle_json notifications/initialized returns nil response" do
+      request = JSON.generate({
+        jsonrpc: "2.0",
+        method: "notifications/initialized",
+      })
+
+      assert_nil @server.handle_json(request)
+      assert_instrumentation_data({ method: "notifications/initialized" })
+    end
+
     test "#handle tools/list returns available tools" do
       request = {
         jsonrpc: "2.0",