fix(pageserver): buffered writer cancellation error handling (#12376)

## Problem

The problem has been well described in already-commited PR #11853.
tl;dr: BufferedWriter is sensitive to cancellation, which the previous
approach was not.

The write path was most affected (ingest & compaction), which was mostly
fixed in #11853:
it introduced `PutError` and mapped instances of `PutError` that were
due to cancellation of underlying buffered writer into
`CreateImageLayersError::Cancelled`.

However, there is a long tail of remaining errors that weren't caught by
#11853 that result in `CompactionError::Other`s, which we log with great
noise.

## Solution

The stack trace logging for CompactionError::Other added in #11853
allows us to chop away at that long tail using the following pattern:
- look at the stack trace
- from leaf up, identify the place where we incorrectly map from the
distinguished variant X indicating cancellation to an `anyhow::Error`
- follow that anyhow further up, ensuring it stays the same anyhow all
the way up in the `CompactionError::Other`
- since it stayed one anyhow chain all the way up, root_cause() will
yield us X
- so, in `log_compaction_error`, add an additional `downcast_ref` check
for X

This PR specifically adds checks for
- the flush task cancelling (FlushTaskError, BlobWriterError)
- opening of the layer writer (GateError)

That should cover all the reports in issues 
- https://github.com/neondatabase/cloud/issues/29434
- https://github.com/neondatabase/neon/issues/12162

## Refs
- follow-up to #11853
- fixup of / fixes https://github.com/neondatabase/neon/issues/11762
- fixes https://github.com/neondatabase/neon/issues/12162
- refs https://github.com/neondatabase/cloud/issues/29434

libs/utils/src/sync/gate.rs

@@ -86,6 +86,14 @@ pub enum GateError {
     GateClosed,
 }
 
+impl GateError {
+    pub fn is_cancel(&self) -> bool {
+        match self {
+            GateError::GateClosed => true,
+        }
+    }
+}
+
 impl Default for Gate {
     fn default() -> Self {
         Self {

pageserver/src/tenant/tasks.rs

@@ -17,14 +17,17 @@ use tracing::*;
 use utils::backoff::exponential_backoff_duration;
 use utils::completion::Barrier;
 use utils::pausable_failpoint;
+use utils::sync::gate::GateError;
 
 use crate::context::{DownloadBehavior, RequestContext};
 use crate::metrics::{self, BackgroundLoopSemaphoreMetricsRecorder, TENANT_TASK_EVENTS};
 use crate::task_mgr::{self, BACKGROUND_RUNTIME, TOKIO_WORKER_THREADS, TaskKind};
+use crate::tenant::blob_io::WriteBlobError;
 use crate::tenant::throttle::Stats;
 use crate::tenant::timeline::CompactionError;
 use crate::tenant::timeline::compaction::CompactionOutcome;
 use crate::tenant::{TenantShard, TenantState};
+use crate::virtual_file::owned_buffers_io::write::FlushTaskError;
 
 /// Semaphore limiting concurrent background tasks (across all tenants).
 ///
@@ -313,7 +316,20 @@ pub(crate) fn log_compaction_error(
             let timeline = root_cause
                 .downcast_ref::<PageReconstructError>()
                 .is_some_and(|e| e.is_stopping());
-            let is_stopping = upload_queue || timeline;
+            let buffered_writer_flush_task_canelled = root_cause
+                .downcast_ref::<FlushTaskError>()
+                .is_some_and(|e| e.is_cancel());
+            let write_blob_cancelled = root_cause
+                .downcast_ref::<WriteBlobError>()
+                .is_some_and(|e| e.is_cancel());
+            let gate_closed = root_cause
+                .downcast_ref::<GateError>()
+                .is_some_and(|e| e.is_cancel());
+            let is_stopping = upload_queue
+                || timeline
+                || buffered_writer_flush_task_canelled
+                || write_blob_cancelled
+                || gate_closed;
 
             if is_stopping {
                 Level::INFO