Pass session id's to MCP endpoints. (#466)

* Pass session id's to MCP endpoints.

* Update src/ModelContextProtocol/Client/McpClient.cs

Co-authored-by: Stephen Halter <halter73@gmail.com>

* Update src/ModelContextProtocol.AspNetCore/StreamableHttpHandler.cs

Co-authored-by: Stephen Halter <halter73@gmail.com>

* Make init callback asynchronous.

* Address feedback.

---------

Co-authored-by: Stephen Halter <halter73@gmail.com>

src/ModelContextProtocol.Core/Protocol/ITransport.cs

@@ -25,6 +25,14 @@ namespace ModelContextProtocol.Protocol;
 /// </remarks>
 public interface ITransport : IAsyncDisposable
 {
+    /// <summary>Gets an identifier associated with the current MCP session.</summary>
+    /// <remarks>
+    /// Typically populated in transports supporting multiple sessions such as Streamable HTTP or SSE.
+    /// Can return <see langword="null"/> if the session hasn't initialized or if the transport doesn't
+    /// support multiple sessions (as is the case with STDIO).
+    /// </remarks>
+    string? SessionId { get; }
+
     /// <summary>
     /// Gets a channel reader for receiving messages from the transport.
     /// </summary>

src/ModelContextProtocol.Core/Protocol/TransportBase.cs

@@ -59,6 +59,9 @@ public abstract partial class TransportBase : ITransport
     /// <summary>Gets the logger used by this transport.</summary>
     private protected ILogger Logger => _logger;
 
+    /// <inheritdoc/>
+    public virtual string? SessionId { get; protected set; }
+
     /// <summary>
     /// Gets the name that identifies this transport endpoint in logs.
     /// </summary>