chore(background_tasks): missed allowed_error change, logging change (#5883)

- I am always confused by the log for the error wait time, now it will
be `2s` or `2.0s` not `2.0`
- fix missed string change introduced in #5881 [evidence]

[evidence]:
https://neon-github-public-dev.s3.amazonaws.com/reports/main/6921062837/index.html#suites/f9eba3cfdb71aa6e2b54f6466222829b/87897fe1ddee3825

pageserver/src/tenant/tasks.rs

@@ -185,11 +185,11 @@ async fn compaction_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                         MAX_BACKOFF_SECS,
                     );
                     error_run_count += 1;
+                    let wait_duration = Duration::from_secs_f64(wait_duration);
                     error!(
-                        "Compaction failed {error_run_count} times, retrying in {:?}: {e:?}",
-                        wait_duration
+                        "Compaction failed {error_run_count} times, retrying in {wait_duration:?}: {e:?}",
                     );
-                    Duration::from_secs_f64(wait_duration)
+                    wait_duration
                 } else {
                     error_run_count = 0;
                     period
@@ -270,11 +270,11 @@ async fn gc_loop(tenant: Arc<Tenant>, cancel: CancellationToken) {
                         MAX_BACKOFF_SECS,
                     );
                     error_run_count += 1;
+                    let wait_duration = Duration::from_secs_f64(wait_duration);
                     error!(
-                        "Gc failed {error_run_count} times, retrying in {:?}: {e:?}",
-                        wait_duration
+                        "Gc failed {error_run_count} times, retrying in {wait_duration:?}: {e:?}",
                     );
-                    Duration::from_secs_f64(wait_duration)
+                    wait_duration
                 } else {
                     error_run_count = 0;
                     period

test_runner/fixtures/neon_fixtures.py

@@ -1663,7 +1663,7 @@ class NeonPageserver(PgProtocol):
             # these can happen anytime we do compactions from background task and shutdown pageserver
             r".*ERROR.*ancestor timeline \S+ is being stopped",
             # this is expected given our collaborative shutdown approach for the UploadQueue
-            ".*Compaction failed.*, retrying in .*: queue is in state Stopped.*",
+            ".*Compaction failed.*, retrying in .*: Other\\(queue is in state Stopped.*",
             # Pageserver timeline deletion should be polled until it gets 404, so ignore it globally
             ".*Error processing HTTP request: NotFound: Timeline .* was not found",
             ".*took more than expected to complete.*",