storcon: use Duration for duration's in the storage controller tenant config (#10928)

## Problem

The storage controller treats durations in the tenant config as strings.
These are loaded from the db.
The pageserver maps these durations to a seconds only format and we
always get a mismatch compared
to what's in the db.

## Summary of changes

Treat durations as durations inside the storage controller and not as
strings.
Nothing changes in the cross service API's themselves or the way things
are stored in the db.

I also added some logging which I would have made the investigation a
10min job:
1. Reason for why the reconciliation was spawned
2. Location config diff between the observed and wanted states

test_runner/regress/test_storage_controller.py

@@ -3817,3 +3817,43 @@ def test_update_node_on_registration(neon_env_builder: NeonEnvBuilder):
     nodes = env.storage_controller.node_list()
     assert len(nodes) == 1
     assert nodes[0]["listen_https_port"] is None
+
+
+def test_storage_controller_location_conf_equivalence(neon_env_builder: NeonEnvBuilder):
+    """
+    Validate that a storage controller restart with no shards in a transient state
+    performs zero reconciliations at start-up. Implicitly, this means that the location
+    configs returned by the pageserver are identical to the persisted state in the
+    storage controller database.
+    """
+    neon_env_builder.num_pageservers = 1
+    neon_env_builder.storage_controller_config = {
+        "start_as_candidate": False,
+    }
+
+    env = neon_env_builder.init_configs()
+    env.start()
+
+    tenant_id = TenantId.generate()
+    env.storage_controller.tenant_create(
+        tenant_id, shard_count=2, tenant_config={"pitr_interval": "1h2m3s"}
+    )
+
+    env.storage_controller.reconcile_until_idle()
+
+    reconciles_before_restart = env.storage_controller.get_metric_value(
+        "storage_controller_reconcile_complete_total", filter={"status": "ok"}
+    )
+
+    assert reconciles_before_restart != 0
+
+    env.storage_controller.stop()
+    env.storage_controller.start()
+
+    env.storage_controller.reconcile_until_idle()
+
+    reconciles_after_restart = env.storage_controller.get_metric_value(
+        "storage_controller_reconcile_complete_total", filter={"status": "ok"}
+    )
+
+    assert reconciles_after_restart == 0