Make it easier to debug integration tests (#4488)

By teeing the output here, something like `bazel test
tests/core/from_go_mod_file:all --test_output=streamed` will now stream
the underlying build progress as one would hope

go/tools/bazel_testing/bazel_testing.go

diff --git a/go/tools/bazel_testing/bazel_testing.go b/go/tools/bazel_testing/bazel_testing.go
index cc31460..40e670c 100644
--- a/go/tools/bazel_testing/bazel_testing.go
+++ b/go/tools/bazel_testing/bazel_testing.go
@@ -26,7 +26,6 @@
 	"flag"
 	"fmt"
 	"io"
-	"io/ioutil"
 	"os"
 	"os/exec"
 	"os/signal"
@@ -205,7 +204,7 @@
 	cmd := BazelCmd(args...)
 
 	buf := &bytes.Buffer{}
-	cmd.Stderr = buf
+	cmd.Stderr = io.MultiWriter(os.Stderr, buf)
 	err := cmd.Run()
 	if eErr, ok := err.(*exec.ExitError); ok {
 		eErr.Stderr = buf.Bytes()
@@ -234,7 +233,7 @@
 	stdout := &bytes.Buffer{}
 	stderr := &bytes.Buffer{}
 	cmd.Stdout = stdout
-	cmd.Stderr = stderr
+	cmd.Stderr = io.MultiWriter(os.Stderr, stderr)
 	if stdin != nil {
 		cmd.Stdin = stdin
 	}
@@ -460,7 +459,7 @@
 				return err
 			}
 		}
-		if err := ioutil.WriteFile(filepath.Join(dir, f.Name), f.Data, 0666); err != nil {
+		if err := os.WriteFile(filepath.Join(dir, f.Name), f.Data, 0666); err != nil {
 			return err
 		}
 	}