pageserver: cancellation handling in writes to postgres client socket (#5503)

## Problem

Writes to the postgres client socket from the page server were not
wrapped in cancellation handling, so a stuck client connection could
prevent tenant shutdowwn.

## Summary of changes

All the places we call flush() to write to the socket, we should be
respecting the cancellation token for the task.

In this PR, I explicitly pass around a CancellationToken rather than
doing inline `task_mgr::shutdown_token` calls, to avoid coupling it to
the global task_mgr state and make it easier to refactor later.

I have some follow-on commits that add a Shutdown variant to QueryError
and use it more extensively, but that's pure refactor so will keep
separate from this bug fix PR.

Closes: https://github.com/neondatabase/neon/issues/5341

libs/postgres_backend/src/lib.rs

@@ -442,10 +442,20 @@ impl<IO: AsyncRead + AsyncWrite + Unpin> PostgresBackend<IO> {
             trace!("got message {:?}", msg);
 
             let result = self.process_message(handler, msg, &mut query_string).await;
-            self.flush().await?;
+            tokio::select!(
+                biased;
+                _ = shutdown_watcher() => {
+                    // We were requested to shut down.
+                    tracing::info!("shutdown request received during response flush");
+                    return Ok(())
+                },
+                flush_r = self.flush() => {
+                    flush_r?;
+                }
+            );
+
             match result? {
                 ProcessMsgResult::Continue => {
-                    self.flush().await?;
                     continue;
                 }
                 ProcessMsgResult::Break => break,