Add a TDD issue-capture test (tagged @tdd_issue, @tdd_issue_10516,
@tdd_expected_fail) that proves the race condition in
McpClient._schedule_idle_timer() where timer.start() is called
outside the lock, allowing a timer to fire even after shutdown()
has called _cancel_idle_timer().

The test uses concurrent scheduling threads to trigger the race
window and verifies that _check_idle() fires when _shutting_down
is True, confirming the bug exists.

Closes #10516

@@ -0,0 +141,4 @@
+
+            # Ensure client is in running state
+            if client.state not in ("running",):
+                from contextlib import suppress as _suppress

@@ -0,0 +34,4 @@
+# See: https://git.cleverthis.com/cleveragents/cleveragents-core/issues/10516
+
+@tdd_issue @tdd_issue_10516
+Feature: TDD Issue #10516 — McpClient timer can fire after cancellation race

@@ -0,0 +75,4 @@
+    When I start the client
+    And I trigger the idle timer race by forcing a reschedule during shutdown
+    And I wait long enough for any late timer fires (0.3s)
+    Then the idle timer callback should not have fired after shutdown

@@ -0,0 +27,4 @@
+import time
+
+from behave import given, then, when
+from behave.runner import Context

@@ -0,0 +33,4 @@
+#
+# See: https://git.cleverthis.com/cleveragents/cleveragents-core/issues/10516
+
+@tdd_issue @tdd_issue_10516