fix(output): print notes to stderr

A note explains the situation around a command rather than being part of its
result, so piping stdout to a file or a parser should not pick it up. Every
current caller is prose for a human: `vp check`'s "Format skipped", the dlx
yarn@1 fallback, "Version will be downloaded on first use", "Restart your
terminal to apply shell changes".

This is also what `rfcs/cli-output-polish.md` specified for `note` in both
Rust and TypeScript; the implementation used `println!` instead.

Author: wan9chi

crates/vite_shared/src/output.rs

@@ -67,14 +67,14 @@ pub fn error(msg: &str) {
     eprintln!("{} {msg}", "error:".red().bold());
 }
 
-/// Print a note message to stdout (supplementary info).
-#[expect(clippy::print_stdout, clippy::print_stderr, clippy::disallowed_macros)]
+/// Print a note message to stderr (supplementary info).
+///
+/// A note explains the situation around a command rather than being part of
+/// its result, so it belongs on the diagnostic stream: piping stdout to a file
+/// or a parser keeps the command's own output intact.
+#[expect(clippy::print_stderr, clippy::disallowed_macros)]
 pub fn note(msg: &str) {
-    if user_output_to_stderr() {
-        eprintln!("{} {msg}", "note:".dimmed().bold());
-    } else {
-        println!("{} {msg}", "note:".dimmed().bold());
-    }
+    eprintln!("{} {msg}", "note:".dimmed().bold());
 }
 
 /// Print a success line with checkmark to stdout.