fix(tests): improve test_scrubber_tenant_snapshot stability (#11471)

## Problem
`test_scrubber_tenant_snapshot` is flaky with `request was dropped`
errors. More details are in the issue.
- Closes: https://github.com/neondatabase/neon/issues/11278

## Summary of changes
- Disable shard scheduling during pageservers restart
- Add `reconcile_until_idle` in the end of the test

storage_controller/src/service.rs

@@ -7270,7 +7270,7 @@ impl Service {
             }
 
             // Eventual consistency: if an earlier reconcile job failed, and the shard is still
-            // dirty, spawn another rone
+            // dirty, spawn another one
             if self
                 .maybe_reconcile_shard(shard, &pageservers, ReconcilerPriority::Normal)
                 .is_some()

test_runner/regress/test_storage_scrubber.py

@@ -75,7 +75,7 @@ def test_scrubber_tenant_snapshot(neon_env_builder: NeonEnvBuilder, shard_count:
         tenant_shard_ids = [TenantShardId(tenant_id, 0, 0)]
 
     # Let shards finish rescheduling to other pageservers: this makes the rest of the test more stable
-    # is it won't overlap with migrations
+    # as it won't overlap with migrations
     env.storage_controller.reconcile_until_idle(max_interval=0.1, timeout_secs=120)
 
     output_path = neon_env_builder.test_output_dir / "snapshot"
@@ -87,6 +87,13 @@ def test_scrubber_tenant_snapshot(neon_env_builder: NeonEnvBuilder, shard_count:
 
     workload.stop()
 
+    # Disable scheduling, so the storage controller doesn't migrate shards around
+    # while we are stopping pageservers
+    env.storage_controller.tenant_policy_update(tenant_id, {"scheduling": "Stop"})
+    env.storage_controller.allowed_errors.extend(
+        [".*Scheduling is disabled by policy Stop.*", ".*Skipping reconcile for policy Stop.*"]
+    )
+
     # Stop pageservers
     for pageserver in env.pageservers:
         pageserver.stop()
@@ -127,9 +134,16 @@ def test_scrubber_tenant_snapshot(neon_env_builder: NeonEnvBuilder, shard_count:
     for pageserver in env.pageservers:
         pageserver.start()
 
+    # Turn scheduling back on.
+    # We don't care about optimizations, so enable only essential scheduling
+    env.storage_controller.tenant_policy_update(tenant_id, {"scheduling": "Essential"})
+
     # Check we can read everything
     workload.validate()
 
+    # Reconcile to avoid a race between test shutdown and background reconciliation (#11278)
+    env.storage_controller.reconcile_until_idle()
+
 
 def drop_local_state(env: NeonEnv, tenant_id: TenantId):
     env.storage_controller.tenant_policy_update(tenant_id, {"placement": "Detached"})