Add tablet index backfill timer (#39120)

GitOrigin-RevId: 13e89eae4a2b6ed154e6c260609832fc76d583b5

Author: emmaling27

crates/database/src/index_worker.rs

@@ -103,6 +103,7 @@ use crate::{
         index_backfill_timer,
         log_index_backfilled,
         log_num_indexes_to_backfill,
+        tablet_index_backfill_timer,
     },
     retention::LeaderRetentionManager,
     Database,
@@ -377,6 +378,7 @@ impl<RT: Runtime> IndexWorker<RT> {
         table_mapping: &TableMapping,
         index_documents: BTreeMap<ResolvedDocumentId, ResolvedDocument>,
     ) -> anyhow::Result<()> {
+        let _timer = tablet_index_backfill_timer();
         let index_registry = IndexRegistry::bootstrap(
             table_mapping,
             index_documents.into_values(),

crates/database/src/metrics.rs

@@ -69,6 +69,14 @@ pub fn index_backfill_timer() -> CancelableTimer {
     CancelableTimer::new(&DB_INDEX_BACKFILL_SECONDS)
 }
 
+register_convex_histogram!(
+    TABLET_DB_INDEX_BACKFILL_SECONDS,
+    "Time for database indexes to backfill",
+);
+pub fn tablet_index_backfill_timer() -> Timer<VMHistogram> {
+    Timer::new(&TABLET_DB_INDEX_BACKFILL_SECONDS)
+}
+
 register_convex_histogram!(
     DATABASE_WRITE_TX_READ_INTERVALS_TOTAL,
     "Number of read intervals in a write transaction"