Filter noisy targets from persistent logs (#29457)

## Why

The local SQLite log sink currently enables TRACE for every target. This
persists high-volume dependency logs bridged through `target=log` and
duplicates OpenTelemetry mirror events in `codex_otel.log_only` and
`codex_otel.trace_safe`.

These records rapidly consume the per-partition log budget and cause
unnecessary SQLite insert-and-prune churn.

## What changed

- Keep TRACE persistence for other targets.
- Exclude bridged `target=log` events from the SQLite sink.
- Exclude the two `codex_otel` mirror targets from the SQLite sink.
- Share the same filter between app-server and TUI.

Remote OpenTelemetry export and metrics are unchanged.

codex-rs/state/src/log_db.rs

@@ -30,11 +30,13 @@ use tokio::sync::oneshot;
 use tracing::Event;
 use tracing::field::Field;
 use tracing::field::Visit;
+use tracing::level_filters::LevelFilter;
 use tracing::span::Attributes;
 use tracing::span::Id;
 use tracing::span::Record;
 use tracing_subscriber::Layer;
 use tracing_subscriber::field::RecordFields;
+use tracing_subscriber::filter::Targets;
 use tracing_subscriber::fmt::FormatFields;
 use tracing_subscriber::fmt::FormattedFields;
 use tracing_subscriber::fmt::format::DefaultFields;
@@ -48,6 +50,14 @@ const LOG_QUEUE_CAPACITY: usize = 512;
 const LOG_BATCH_SIZE: usize = 128;
 const LOG_FLUSH_INTERVAL: Duration = Duration::from_secs(2);
 
+pub fn default_filter() -> Targets {
+    Targets::new()
+        .with_default(LevelFilter::TRACE)
+        .with_target("log", LevelFilter::OFF)
+        .with_target("codex_otel.log_only", LevelFilter::OFF)
+        .with_target("codex_otel.trace_safe", LevelFilter::OFF)
+}
+
 #[derive(Clone, Copy, Debug, Eq, PartialEq)]
 pub struct LogSinkQueueConfig {
     pub queue_capacity: usize,