save: print to stderr for bytestream (#13422)

# Description
Fixes: #13260 

When user run a command like this:
```nushell
$env.FOO = " New";
$env.BAZ = " New Err";
do -i {nu -n -c 'nu --testbin echo_env FOO; nu --testbin echo_env_stderr BAZ'} | save -a -r save_test_22/log.txt
```

`save` command sinks the output of previous commands' stderr output. I
think it should be `stderr`.

# User-Facing Changes
```nushell
$env.FOO = " New";
$env.BAZ = " New Err";
do -i {nu -n -c 'nu --testbin echo_env FOO; nu --testbin echo_env_stderr BAZ'} | save -a -r save_test_22/log.txt
```
The command will output ` New Err` to stderr.

# Tests + Formatting
Added 2 cases.

crates/nu-command/src/filesystem/save.rs

@@ -121,9 +121,11 @@ impl Command for Save {
                             } else {
                                 match stderr {
                                     ChildPipe::Pipe(mut pipe) => {
-                                        io::copy(&mut pipe, &mut io::sink())
+                                        io::copy(&mut pipe, &mut io::stderr())
+                                    }
+                                    ChildPipe::Tee(mut tee) => {
+                                        io::copy(&mut tee, &mut io::stderr())
                                     }
-                                    ChildPipe::Tee(mut tee) => io::copy(&mut tee, &mut io::sink()),
                                 }
                                 .err_span(span)?;
                             }

crates/nu-command/tests/commands/save.rs

@@ -463,3 +463,65 @@ fn save_same_file_with_collect_and_filter() {
         assert_eq!("helloworld", actual.out);
     })
 }
+
+#[test]
+fn save_from_child_process_dont_sink_stderr() {
+    Playground::setup("save_test_22", |dirs, sandbox| {
+        sandbox.with_files(&[
+            Stub::FileWithContent("log.txt", "Old"),
+            Stub::FileWithContent("err.txt", "Old Err"),
+        ]);
+
+        let expected_file = dirs.test().join("log.txt");
+        let expected_stderr_file = dirs.test().join("err.txt");
+
+        let actual = nu!(
+            cwd: dirs.root(),
+            r#"
+            $env.FOO = " New";
+            $env.BAZ = " New Err";
+            do -i {nu -n -c 'nu --testbin echo_env FOO; nu --testbin echo_env_stderr BAZ'} | save -a -r save_test_22/log.txt"#,
+        );
+        assert_eq!(actual.err.trim_end(), " New Err");
+
+        let actual = file_contents(expected_file);
+        assert_eq!(actual.trim_end(), "Old New");
+
+        let actual = file_contents(expected_stderr_file);
+        assert_eq!(actual.trim_end(), "Old Err");
+    })
+}
+
+#[test]
+fn parent_redirection_doesnt_affect_save() {
+    Playground::setup("save_test_23", |dirs, sandbox| {
+        sandbox.with_files(&[
+            Stub::FileWithContent("log.txt", "Old"),
+            Stub::FileWithContent("err.txt", "Old Err"),
+        ]);
+
+        let expected_file = dirs.test().join("log.txt");
+        let expected_stderr_file = dirs.test().join("err.txt");
+
+        let actual = nu!(
+            cwd: dirs.root(),
+            r#"
+            $env.FOO = " New";
+            $env.BAZ = " New Err";
+            def tttt [] {
+                do -i {nu -n -c 'nu --testbin echo_env FOO; nu --testbin echo_env_stderr BAZ'} | save -a -r save_test_23/log.txt
+            };
+            tttt e> ("save_test_23" | path join empty_file)"#
+        );
+        assert_eq!(actual.err.trim_end(), " New Err");
+
+        let actual = file_contents(expected_file);
+        assert_eq!(actual.trim_end(), "Old New");
+
+        let actual = file_contents(expected_stderr_file);
+        assert_eq!(actual.trim_end(), "Old Err");
+
+        let actual = file_contents(dirs.test().join("empty_file"));
+        assert_eq!(actual.trim_end(), "");
+    })
+}