feat: add structured logging support with severity levels

- Add client and server-side logging capabilities with configurable severity levels
- Implement logging message notifications with DEBUG to EMERGENCY levels
- Add logging consumers for client-side log handling
- Update documentation with logging examples and configuration
- Add comprehensive tests for logging functionality
- Fix typo in README.md (notificaiotn -> notification)

- Centralize MCP method names as constants
  - Move all JSON-RPC method names to McpSchema class as static constants
  - Replace hardcoded method strings with constant references in McpAsyncClient
    and McpAsyncServer
  - Update test cases to use new method name constants

Resolves #35

spring-ai-mcp-sample/src/main/java/org/springframework/ai/mcp/sample/server/McpServerConfig.java

@@ -4,6 +4,8 @@ import java.util.List;
 import java.util.Map;
 
 import com.fasterxml.jackson.databind.ObjectMapper;
+import org.slf4j.Logger;
+import org.slf4j.LoggerFactory;
 
 import org.springframework.ai.mcp.server.McpAsyncServer;
 import org.springframework.ai.mcp.server.McpServer;
@@ -15,6 +17,7 @@ import org.springframework.ai.mcp.server.transport.StdioServerTransport;
 import org.springframework.ai.mcp.spec.McpSchema;
 import org.springframework.ai.mcp.spec.McpSchema.CallToolResult;
 import org.springframework.ai.mcp.spec.McpSchema.GetPromptResult;
+import org.springframework.ai.mcp.spec.McpSchema.LoggingMessageNotification;
 import org.springframework.ai.mcp.spec.McpSchema.PromptMessage;
 import org.springframework.ai.mcp.spec.McpSchema.Role;
 import org.springframework.ai.mcp.spec.McpSchema.TextContent;
@@ -27,6 +30,8 @@ import org.springframework.web.reactive.function.server.RouterFunction;
 @Configuration
 public class McpServerConfig {
 
+	private static final Logger logger = LoggerFactory.getLogger(McpServerConfig.class);
+
 	// STDIO transport
 	@Bean
 	@ConditionalOnProperty(prefix = "transport", name = "mode", havingValue = "stdio")
@@ -41,7 +46,8 @@ public class McpServerConfig {
 		return new SseServerTransport(new ObjectMapper(), "/mcp/message");
 	}
 
-	// Router function for SSE transport used by Spring WebFlux to start an HTTP server.
+	// Router function for SSE transport used by Spring WebFlux to start an HTTP
+	// server.
 	@Bean
 	@ConditionalOnProperty(prefix = "transport", name = "mode", havingValue = "sse")
 	public RouterFunction<?> mcpRouterFunction(SseServerTransport transport) {
@@ -56,16 +62,20 @@ public class McpServerConfig {
 			.resources(false, true) // No subscribe support, but list changes notifications
 			.tools(true) // Tool support with list changes notifications
 			.prompts(true) // Prompt support with list changes notifications
+			.logging() // Logging support
 			.build();
 
 		// Create the server with both tool and resource capabilities
-		return McpServer.using(transport)
+		var server = McpServer.using(transport)
 			.info("MCP Demo Server", "1.0.0")
 			.capabilities(capabilities)
 			.resources(systemInfoResourceRegistration())
 			.prompts(greetingPromptRegistration())
-			.tools(weatherToolRegistration(), calculatorToolRegistration())
+			.tools(calculatorToolRegistration())
 			.async();
+		
+		server.addTool(weatherToolRegistration(server));
+		return server; // @formatter:on
 	} // @formatter:on
 
 	private static ResourceRegistration systemInfoResourceRegistration() {
@@ -120,13 +130,27 @@ public class McpServerConfig {
 		});
 	}
 
-	private static ToolRegistration weatherToolRegistration() {
+	private static ToolRegistration weatherToolRegistration(McpAsyncServer server) {
 		return new ToolRegistration(
 				new McpSchema.Tool("weather", "Weather forecast tool by location", Map.of("city", "String")),
 				(arguments) -> {
 					String city = (String) arguments.get("city");
-					TextContent content = new TextContent("Weather forecast for " + city + " is sunny");
-					return new CallToolResult(List.of(content), false);
+
+					// Create the result
+					var result = new CallToolResult(
+							List.of(new TextContent("Weather forecast for " + city + " is sunny")), false);
+
+					// Send the logging notification and ignore its completion
+					server
+						.loggingNotification(LoggingMessageNotification.builder()
+							.data("This is a log message from the weather tool")
+							.build())
+						.subscribe(null, error -> {
+							// Log any errors but don't fail the operation
+							logger.error("Failed to send logging notification", error);
+						});
+
+					return result;
 				});
 	}