pageserver: tweaks to slow/hung task logging (#6098)

## Problem

- `shutdown_tasks` would log when a particular task was taking a long
time to shut down, but not when it eventually completed. That left one
uncertain as to whether the slow task was the source of a hang, or just
a precursor.

## Summary of changes

- Add a log line after a slow task shutdown
- Add an equivalent in Gate's `warn_if_stuck`, in case we ever need it.
This isn't related to the original issue but was noticed when checking
through these logging paths.

libs/utils/src/sync/gate.rs

@@ -30,18 +30,32 @@ async fn warn_if_stuck<Fut: std::future::Future>(
 
     let mut fut = std::pin::pin!(fut);
 
-    loop {
+    let mut warned = false;
+    let ret = loop {
         match tokio::time::timeout(warn_period, &mut fut).await {
-            Ok(ret) => return ret,
+            Ok(ret) => break ret,
             Err(_) => {
                 tracing::warn!(
                     gate = name,
                     elapsed_ms = started.elapsed().as_millis(),
                     "still waiting, taking longer than expected..."
                 );
+                warned = true;
             }
         }
+    };
+
+    // If we emitted a warning for slowness, also emit a message when we complete, so that
+    // someone debugging a shutdown can know for sure whether we have moved past this operation.
+    if warned {
+        tracing::info!(
+            gate = name,
+            elapsed_ms = started.elapsed().as_millis(),
+            "completed, after taking longer than expected"
+        )
     }
+
+    ret
 }
 
 #[derive(Debug)]

pageserver/src/task_mgr.rs

@@ -518,12 +518,13 @@ pub async fn shutdown_tasks(
             {
                 // allow some time to elapse before logging to cut down the number of log
                 // lines.
-                info!("waiting for {} to shut down", task.name);
+                info!("waiting for task {} to shut down", task.name);
                 // we never handled this return value, but:
                 // - we don't deschedule which would lead to is_cancelled
                 // - panics are already logged (is_panicked)
                 // - task errors are already logged in the wrapper
                 let _ = join_handle.await;
+                info!("task {} completed", task.name);
             }
         } else {
             // Possibly one of: