mcp: fix context propagation in StreamableClientTransport (#514)

## Problem
Context propagation was broken in `StreamableClientTransport` because:
1. `Connect()` used `context.Background()` instead of the parent context
2. `Close()` created a race condition where DELETE requests were
cancelled before completion

## Solution  
- Use parent context when creating the connection context in `Connect()`
- Reorder `Close()` operations to perform cleanup DELETE before
cancelling context

## Impact
- Request-scoped values (auth tokens, trace IDs) now propagate correctly
to background HTTP operations
- Eliminates race condition in cleanup operations  
- Maintains proper Go context semantics

Fixes #513

mcp/streamable.go

@@ -1018,7 +1018,7 @@ func (t *StreamableClientTransport) Connect(ctx context.Context) (Connection, er
 	// Create a new cancellable context that will manage the connection's lifecycle.
 	// This is crucial for cleanly shutting down the background SSE listener by
 	// cancelling its blocking network operations, which prevents hangs on exit.
-	connCtx, cancel := context.WithCancel(context.Background())
+	connCtx, cancel := context.WithCancel(ctx)
 	conn := &streamableClientConn{
 		url:        t.Endpoint,
 		client:     client,
@@ -1230,7 +1230,7 @@ func (c *streamableClientConn) Write(ctx context.Context, msg jsonrpc.Message) e
 
 // testAuth controls whether a fake Authorization header is added to outgoing requests.
 // TODO: replace with a better mechanism when client-side auth is in place.
-var testAuth = false
+var testAuth atomic.Bool
 
 func (c *streamableClientConn) setMCPHeaders(req *http.Request) {
 	c.mu.Lock()
@@ -1242,7 +1242,7 @@ func (c *streamableClientConn) setMCPHeaders(req *http.Request) {
 	if c.sessionID != "" {
 		req.Header.Set(sessionIDHeader, c.sessionID)
 	}
-	if testAuth {
+	if testAuth.Load() {
 		req.Header.Set("Authorization", "Bearer foo")
 	}
 }
@@ -1394,14 +1394,10 @@ func (c *streamableClientConn) reconnect(lastEventID string) (*http.Response, er
 // Close implements the [Connection] interface.
 func (c *streamableClientConn) Close() error {
 	c.closeOnce.Do(func() {
-		// Cancel any hanging network requests.
-		c.cancel()
-		close(c.done)
-
 		if errors.Is(c.failure(), errSessionMissing) {
 			// If the session is missing, no need to delete it.
 		} else {
-			req, err := http.NewRequest(http.MethodDelete, c.url, nil)
+			req, err := http.NewRequestWithContext(c.ctx, http.MethodDelete, c.url, nil)
 			if err != nil {
 				c.closeErr = err
 			} else {
@@ -1411,6 +1407,10 @@ func (c *streamableClientConn) Close() error {
 				}
 			}
 		}
+
+		// Cancel any hanging network requests after cleanup.
+		c.cancel()
+		close(c.done)
 	})
 	return c.closeErr
 }