feat: backfill timing metric (#10218)

1. Add a metric to measure the backfill time
2. Add a unit to the timing histogram

codex-rs/core/src/rollout/metadata.rs

@@ -16,6 +16,7 @@ use codex_protocol::protocol::SessionSource;
 use codex_state::BackfillStats;
 use codex_state::DB_ERROR_METRIC;
 use codex_state::DB_METRIC_BACKFILL;
+use codex_state::DB_METRIC_BACKFILL_DURATION_MS;
 use codex_state::ExtractionOutcome;
 use codex_state::ThreadMetadataBuilder;
 use codex_state::apply_rollout_item;
@@ -128,6 +129,7 @@ pub(crate) async fn backfill_sessions(
     config: &Config,
     otel: Option<&OtelManager>,
 ) {
+    let timer = otel.and_then(|otel| otel.start_timer(DB_METRIC_BACKFILL_DURATION_MS, &[]).ok());
     let sessions_root = config.codex_home.join(rollout::SESSIONS_SUBDIR);
     let archived_root = config.codex_home.join(rollout::ARCHIVED_SESSIONS_SUBDIR);
     let mut rollout_paths: Vec<(PathBuf, bool)> = Vec::new();
@@ -210,6 +212,16 @@ pub(crate) async fn backfill_sessions(
             &[("status", "failed")],
         );
     }
+    if let Some(timer) = timer.as_ref() {
+        let status = if stats.failed == 0 {
+            "success"
+        } else if stats.upserted == 0 {
+            "failed"
+        } else {
+            "partial_failure"
+        };
+        let _ = timer.record(&[("status", status)]);
+    }
 }
 
 async fn file_modified_time_utc(path: &Path) -> Option<DateTime<Utc>> {