pageserver: add initdb metrics (#10434)

## Problem

Initdb observability is poor.

## Summary of changes

Add some metrics so we can figure out which part, if any, is slow.

Closes https://github.com/neondatabase/neon/issues/10423

pageserver/src/metrics.rs

@@ -100,6 +100,32 @@ pub(crate) static VEC_READ_NUM_LAYERS_VISITED: Lazy<Histogram> = Lazy::new(|| {
     .expect("failed to define a metric")
 });
 
+pub(crate) static CONCURRENT_INITDBS: Lazy<UIntGauge> = Lazy::new(|| {
+    register_uint_gauge!(
+        "pageserver_concurrent_initdb",
+        "Number of initdb processes running"
+    )
+    .expect("failed to define a metric")
+});
+
+pub(crate) static INITDB_SEMAPHORE_ACQUISITION_TIME: Lazy<Histogram> = Lazy::new(|| {
+    register_histogram!(
+        "pageserver_initdb_semaphore_seconds_global",
+        "Time spent getting a permit from the global initdb semaphore",
+        STORAGE_OP_BUCKETS.into()
+    )
+    .expect("failed to define metric")
+});
+
+pub(crate) static INITDB_RUN_TIME: Lazy<Histogram> = Lazy::new(|| {
+    register_histogram!(
+        "pageserver_initdb_seconds_global",
+        "Time spent performing initdb",
+        STORAGE_OP_BUCKETS.into()
+    )
+    .expect("failed to define metric")
+});
+
 // Metrics collected on operations on the storage repository.
 #[derive(
     Clone, Copy, enum_map::Enum, strum_macros::EnumString, strum_macros::Display, IntoStaticStr,

pageserver/src/tenant.rs

@@ -95,6 +95,9 @@ use crate::deletion_queue::DeletionQueueError;
 use crate::import_datadir;
 use crate::is_uninit_mark;
 use crate::l0_flush::L0FlushGlobalState;
+use crate::metrics::CONCURRENT_INITDBS;
+use crate::metrics::INITDB_RUN_TIME;
+use crate::metrics::INITDB_SEMAPHORE_ACQUISITION_TIME;
 use crate::metrics::TENANT;
 use crate::metrics::{
     remove_tenant_metrics, BROKEN_TENANTS_SET, CIRCUIT_BREAKERS_BROKEN, CIRCUIT_BREAKERS_UNBROKEN,
@@ -5347,8 +5350,17 @@ async fn run_initdb(
         initdb_bin_path, initdb_target_dir, initdb_lib_dir,
     );
 
-    let _permit = INIT_DB_SEMAPHORE.acquire().await;
+    let _permit = {
+        let _timer = INITDB_SEMAPHORE_ACQUISITION_TIME.start_timer();
+        INIT_DB_SEMAPHORE.acquire().await
+    };
 
+    CONCURRENT_INITDBS.inc();
+    scopeguard::defer! {
+        CONCURRENT_INITDBS.dec();
+    }
+
+    let _timer = INITDB_RUN_TIME.start_timer();
     let res = postgres_initdb::do_run_initdb(postgres_initdb::RunInitdbArgs {
         superuser: &conf.superuser,
         locale: &conf.locale,