Add McpTransportContext to McpSyncClient (#522)

* McpSyncClient: introduce McpTransportContext

- McpSyncClient should be considered thread-agnostic, and therefore
  consumers cannot rely on thread locals to propagate "context", e.g.
  pass down the Servlet request reference in a server context.
- This PR introduces a mechanism for populating an McpTransportContext
  before executing client operations, and reworks the HTTP request
  customizers to leverage that McpTransportContext.
- Move McpTransportContext from server to common package for shared client/server usage
- Make McpTransportContext immutable by removing put() and copy() methods
- Add static create() factory method for creating contexts with predefined data
- Update McpTransportContextExtractor to return context instead of modifying one
- Replace DefaultMcpTransportContext mutable implementation with immutable version
- Update all transport implementations to use McpTransportContext.EMPTY as default
- Rename *HttpRequestCustomizer -> *HttpClientRequestCustomizer
- Add end-to-end McpTransportContextIntegrationTests
- This PR introduces a breaking change to the Sync/Async request
  customizers.

Signed-off-by: Daniel Garnier-Moiroux <git@garnier.wf>

mcp-test/src/main/java/io/modelcontextprotocol/AbstractMcpClientServerIntegrationTests.java

@@ -33,11 +33,11 @@ import org.junit.jupiter.params.ParameterizedTest;
 import org.junit.jupiter.params.provider.ValueSource;
 
 import io.modelcontextprotocol.client.McpClient;
+import io.modelcontextprotocol.common.McpTransportContext;
 import io.modelcontextprotocol.server.McpServer;
 import io.modelcontextprotocol.server.McpServerFeatures;
 import io.modelcontextprotocol.server.McpSyncServer;
 import io.modelcontextprotocol.server.McpSyncServerExchange;
-import io.modelcontextprotocol.server.McpTransportContext;
 import io.modelcontextprotocol.spec.McpError;
 import io.modelcontextprotocol.spec.McpSchema;
 import io.modelcontextprotocol.spec.McpSchema.CallToolResult;