fix(runi-log): write logs to stderr (#17)

## Summary
- `init_with_env` uses `IsTerminal` on stderr to choose human vs JSON
format, but `fmt::layer()` defaults to **stdout** — so a `2>log`
redirect would ship JSON to stdout while the TTY check still saw a
terminal.
- Pin all three layers (`init_with_env` TTY, `init_with_env` non-TTY,
`init_with_level`) to `std::io::stderr` so the writer and the terminal
check agree, and match the usual CLI convention of logs-on-stderr.

## Test plan
- [x] `cargo build -p runi-log --all-targets`
- [x] `cargo test -p runi-log`
- [x] `cargo clippy -p runi-log --all-targets -- -D warnings`
- [x] `cargo fmt --all -- --check`

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: xerial

runi-log/src/lib.rs

@@ -25,14 +25,19 @@ pub fn init_with_env(env_var: &str) {
     if is_terminal {
         tracing_subscriber::registry()
             .with(filter)
-            .with(fmt::layer().event_format(UniFormatter::new(true)))
+            .with(
+                fmt::layer()
+                    .with_writer(std::io::stderr)
+                    .event_format(UniFormatter::new(true)),
+            )
             .init();
     } else {
         tracing_subscriber::registry()
             .with(filter)
             .with(
                 fmt::layer()
                     .json()
+                    .with_writer(std::io::stderr)
                     .with_target(true)
                     .with_file(true)
                     .with_line_number(true),
@@ -46,7 +51,11 @@ pub fn init_with_level(level: &str) {
     let filter = EnvFilter::new(level);
     tracing_subscriber::registry()
         .with(filter)
-        .with(fmt::layer().event_format(UniFormatter::new(true)))
+        .with(
+            fmt::layer()
+                .with_writer(std::io::stderr)
+                .event_format(UniFormatter::new(true)),
+        )
         .init();
 }