fix: doh use NewRequestWithContext and batchExchange don't wait cancel finish

dns/doh.go

@@ -208,14 +208,13 @@ func (doh *dnsOverHTTPS) exchangeHTTPSClient(
 	}
 
 	doh.url.RawQuery = fmt.Sprintf("dns=%s", base64.RawURLEncoding.EncodeToString(buf))
-	httpReq, err := http.NewRequest(method, doh.url.String(), nil)
+	httpReq, err := http.NewRequestWithContext(ctx, method, doh.url.String(), nil)
 	if err != nil {
 		return nil, fmt.Errorf("creating http request to %s: %w", doh.url, err)
 	}
 
 	httpReq.Header.Set("Accept", "application/dns-message")
 	httpReq.Header.Set("User-Agent", "")
-	_ = httpReq.WithContext(ctx)
 	httpResp, err := client.Do(httpReq)
 	if err != nil {
 		return nil, fmt.Errorf("requesting %s: %w", doh.url, err)

dns/util.go

@@ -216,7 +216,7 @@ func batchExchange(ctx context.Context, clients []dnsClient, m *D.Msg) (msg *D.M
 	fast, ctx := picker.WithTimeout[*D.Msg](ctx, resolver.DefaultDNSTimeout)
 	for _, client := range clients {
 		r := client
-		fast.Go(func() (*D.Msg, error) {
+		fn := func() (*D.Msg, error) {
 			m, err := r.ExchangeContext(ctx, m)
 			if err != nil {
 				return nil, err
@@ -224,6 +224,27 @@ func batchExchange(ctx context.Context, clients []dnsClient, m *D.Msg) (msg *D.M
 				return nil, errors.New("server failure")
 			}
 			return m, nil
+		}
+		fast.Go(func() (*D.Msg, error) {
+			ch := make(chan result, 1)
+			go func() {
+				m, err := fn()
+				ch <- result{
+					Msg:   m,
+					Error: err,
+				}
+			}()
+			select {
+			case r := <-ch:
+				return r.Msg, r.Error
+			case <-ctx.Done():
+				select {
+				case r := <-ch:
+					return r.Msg, r.Error
+				default:
+					return nil, ctx.Err()
+				}
+			}
 		})
 	}