Fix stdio mode: write responses to stdout, not stdin

In stdio mode, the server should read from stdin and write to stdout.
Previously, we were passing stdin as the client and writing to it,
which doesn't work. Now we detect when client is stdin and write
responses to stdout instead.

This fixes the issue where the server would close immediately after
sending the first response.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: Keno

src/server.jl

@@ -122,8 +122,10 @@ function handle_client_connection(client::IO, server::ClaudeMCPTools.MCPServer;
                 end
 
                 # Send response
-                println(client, json_response)
-                flush(client)
+                # In stdio mode, read from stdin but write to stdout
+                output_stream = (client === stdin) ? stdout : client
+                println(output_stream, json_response)
+                flush(output_stream)
             catch e
                 # Only send error response if it's not a notification
                 if request !== nothing && haskey(request, "id")
@@ -135,8 +137,10 @@ function handle_client_connection(client::IO, server::ClaudeMCPTools.MCPServer;
                         ),
                         "id" => request["id"]
                     )
-                    println(client, JSON.json(error_response))
-                    flush(client)
+                    # In stdio mode, read from stdin but write to stdout
+                    output_stream = (client === stdin) ? stdout : client
+                    println(output_stream, JSON.json(error_response))
+                    flush(output_stream)
                 end
             end
         end