feat(client): Improve initialization state handling in McpAsyncClient (#39)

- Add proper initialization state tracking using AtomicBoolean and Sinks
- Implement timeout handling for requests requiring initialization
- Ensure all client methods verify initialization state before proceeding
- Fix rootsListChangedNotification to check initialization state
- Improve error messages for uninitialized client operations
- improve JavaDoc
- Add tests to verify proper error handling for uninitialized clients
  - Replace hardcoded timeout constants with configurable getTimeoutDuration() method
  - Remove automatic initialization in setUp methods to allow explicit testing

Signed-off-by: Christian Tzolov <christian.tzolov@broadcom.com>

mcp-spring/mcp-spring-webflux/src/test/java/io/modelcontextprotocol/client/WebFluxSseMcpAsyncClientTests.java

@@ -4,6 +4,8 @@
 
 package io.modelcontextprotocol.client;
 
+import java.time.Duration;
+
 import io.modelcontextprotocol.client.transport.WebFluxSseClientTransport;
 import io.modelcontextprotocol.spec.ClientMcpTransport;
 import org.junit.jupiter.api.Timeout;
@@ -46,4 +48,9 @@ class WebFluxSseMcpAsyncClientTests extends AbstractMcpAsyncClientTests {
 		container.stop();
 	}
 
+	@Override
+	protected Duration getTimeoutDuration() {
+		return Duration.ofMillis(300);
+	}
+
 }

mcp-spring/mcp-spring-webflux/src/test/java/io/modelcontextprotocol/client/WebFluxSseMcpSyncClientTests.java

@@ -4,6 +4,8 @@
 
 package io.modelcontextprotocol.client;
 
+import java.time.Duration;
+
 import io.modelcontextprotocol.client.transport.WebFluxSseClientTransport;
 import io.modelcontextprotocol.spec.ClientMcpTransport;
 import org.junit.jupiter.api.Timeout;
@@ -46,4 +48,9 @@ class WebFluxSseMcpSyncClientTests extends AbstractMcpSyncClientTests {
 		container.stop();
 	}
 
+	@Override
+	protected Duration getTimeoutDuration() {
+		return Duration.ofMillis(300);
+	}
+
 }