fix(router): handle None values in update_settings integer settings

Router.update_settings() raised an unhandled TypeError when None was
passed for any integer setting (timeout, num_retries, retry_after,
allowed_fails, cooldown_time):

    _casted_value = int(kwargs[var])   # int(None) -> TypeError

This is a real production path: the proxy server calls
update_settings(**combined_router_settings) on every startup, where
settings are merged from config.yaml and a JSON database. JSON null
maps to Python None, so clearing a timeout via the admin UI causes a
proxy startup crash.

Fix: guard with an explicit None check before casting.

Adds regression test covering all five int settings with None input
and confirms valid int values still work after a None reset.

litellm/router.py

@@ -9520,8 +9520,10 @@ class Router:
         for var in kwargs:
             if var in _allowed_settings:
                 if var in _int_settings:
-                    _casted_value = int(kwargs[var])
-                    setattr(self, var, _casted_value)
+                    if kwargs[var] is None:
+                        setattr(self, var, None)
+                    else:
+                        setattr(self, var, int(kwargs[var]))
                 elif var == "routing_groups":
                     self._routing_groups_input = kwargs[var]
                     rebuild_routing_groups = True

tests/router_unit_tests/test_router_helper_utils.py

@@ -977,6 +977,29 @@ def test_update_settings(model_list):
     assert router.allowed_fails == 20
 
 
+def test_update_settings_none_int_values(model_list):
+    """Regression test: update_settings must not crash when None is passed for int settings.
+    Previously raised TypeError: int() argument must be a string... not 'NoneType'"""
+    router = Router(model_list=model_list, timeout=30, allowed_fails=5)
+
+    # None should reset each int setting without raising TypeError
+    router.update_settings(timeout=None)
+    assert router.timeout is None
+
+    router.update_settings(allowed_fails=None)
+    assert router.allowed_fails is None
+
+    router.update_settings(num_retries=None)
+    assert router.num_retries is None
+
+    router.update_settings(cooldown_time=None)
+    assert router.cooldown_time is None
+
+    # Valid int values must still work after None resets
+    router.update_settings(timeout=60)
+    assert router.timeout == 60
+
+
 def test_common_checks_available_deployment(model_list):
     """Test if the 'common_checks_available_deployment' function is working correctly"""
     router = Router(model_list=model_list)