Web-standard SSE responses override the HTTP server keep-alive lifetime #2553

Problem

WebStandardStreamableHTTPServerTransport sets Connection: keep-alive on each SSE Response, but it cannot know the lifetime of the underlying HTTP connection and does not provide a matching Keep-Alive lifetime.

Connection is a hop-by-hop header. The HTTP adapter or server owns that policy. On Node HTTP/1.1, the explicit SDK header suppresses Node automatic output such as:

Connection: keep-alive
Keep-Alive: timeout=5

Without the lifetime hint, a pooling client cannot retire an idle socket before the server does and can race a server FIN on a later MCP request. On HTTP/2, Connection is forbidden and must be removed by the adapter.

The header is currently present at three response sites on both main and v1.x.

Expected behavior

The web-standard transport should omit hop-by-hop connection policy. The concrete adapter can then describe the real transport:

• Node HTTP/1.1 emits Connection: keep-alive and its configured Keep-Alive: timeout=... automatically.
• HTTP/2 emits neither forbidden hop-by-hop header.
• Other Fetch runtimes remain free to apply their own connection policy.

This does not disable persistent connections and does not require Connection: close. Nearby MCP requests can still reuse a socket, while clients that honor the advertised lifetime can retire it safely and continue the same Mcp-Session-Id on another socket.

Scope

This is separate from SSE comment heartbeats such as #2541. Heartbeats protect an open, temporarily silent SSE body. This issue concerns the idle lifetime of an HTTP connection after a finite response has completed.