Limit RMCP logs persisted to SQLite (#36904)

## What changed

- Persist `rmcp` and `codex_rmcp_client` events only at `INFO` level or above.
- Cover nested targets from both namespaces in the SQLite log filter test.

GitOrigin-RevId: dfeeec302a9562f533a09a735b392d202c1f7801

codex-rs/state/src/log_db.rs

@@ -55,9 +55,10 @@ pub fn default_filter() -> Targets {
         .with_default(LevelFilter::TRACE)
         .with_target("hyper_util", LevelFilter::WARN)
         .with_target("log", LevelFilter::OFF)
+        .with_target("codex_rmcp_client", LevelFilter::INFO)
         .with_target("codex_otel.log_only", LevelFilter::OFF)
         .with_target("codex_otel.trace_safe", LevelFilter::OFF)
-        .with_target("rmcp::service", LevelFilter::INFO)
+        .with_target("rmcp", LevelFilter::INFO)
         .with_target("codex_api::responses_websocket_timing", LevelFilter::OFF)
         .with_target("codex_core::post_sampling_token_estimate", LevelFilter::OFF)
 }

codex-rs/state/src/log_db_filter_tests.rs

@@ -25,6 +25,16 @@ async fn sqlite_sink_drops_low_level_opentelemetry_sdk_logs() {
     tracing::trace!(target: "opentelemetry_sdk", "dropped-trace");
     tracing::debug!(target: "opentelemetry_sdk", "dropped-debug");
     tracing::info!(target: "opentelemetry_sdk", "retained-info");
+    tracing::debug!(target: "rmcp::transport", "dropped-rmcp-debug");
+    tracing::info!(target: "rmcp::transport", "retained-rmcp-info");
+    tracing::debug!(
+        target: "codex_rmcp_client::oauth",
+        "dropped-codex-rmcp-client-debug"
+    );
+    tracing::info!(
+        target: "codex_rmcp_client::oauth",
+        "retained-codex-rmcp-client-info"
+    );
     tracing::trace!(target: "codex_state", "retained-trace");
     tracing::trace!(
         target: "codex_api::responses_websocket_timing",
@@ -49,6 +59,12 @@ async fn sqlite_sink_drops_low_level_opentelemetry_sdk_logs() {
             .collect::<Vec<_>>(),
         vec![
             ("INFO", "opentelemetry_sdk", Some("retained-info")),
+            ("INFO", "rmcp::transport", Some("retained-rmcp-info")),
+            (
+                "INFO",
+                "codex_rmcp_client::oauth",
+                Some("retained-codex-rmcp-client-info")
+            ),
             ("TRACE", "codex_state", Some("retained-trace")),
         ]
     );