fix(health-check-routing): fix three CI failures

- Add "exception" to ILLEGAL_DISPLAY_PARAMS in health_check.py so the
  exception object is stripped before the health endpoint serializes
  results to JSON (fixes TypeError: 'URL' object is not iterable)
- Add allowed_fails_policy = None to FakeRouter stubs in
  test_router_health_check_routing.py (fixes AttributeError)
- Add health_check_ignore_transient_errors to config_settings.md router
  settings reference table (fixes documentation test)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

docs/my-website/docs/proxy/config_settings.md

@@ -367,6 +367,9 @@ router_settings:
 | ignore_invalid_deployments | boolean | If true, ignores invalid deployments. Default for proxy is True - to prevent invalid models from blocking other models from being loaded. |
 | search_tools | List[SearchToolTypedDict] | List of search tool configurations for Search API integration. Each tool specifies a search_tool_name and litellm_params with search_provider, api_key, api_base, etc. [Further Docs](../search/index.md) |
 | guardrail_list | List[GuardrailTypedDict] | List of guardrail configurations for guardrail load balancing. Enables load balancing across multiple guardrail deployments with the same guardrail_name. [Further Docs](./guardrails/guardrail_load_balancing.md) |
+| enable_health_check_routing | boolean | If true, enables health check-driven deployment filtering to avoid routing requests to unhealthy deployments |
+| health_check_staleness_threshold | integer | Maximum age in seconds for cached health check results before marking deployments as stale |
+| health_check_ignore_transient_errors | boolean | If true, 429 (rate limit) and 408 (timeout) health check failures are ignored and do not affect routing or cooldown |
 
 
 ### environment variables - Reference

litellm/proxy/health_check.py

@@ -21,6 +21,7 @@ ILLEGAL_DISPLAY_PARAMS = [
     "vertex_credentials",
     "aws_access_key_id",
     "aws_secret_access_key",
+    "exception",  # internal; not JSON-serializable, never for display
 ]
 
 MINIMAL_DISPLAY_PARAMS = ["model", "mode_error"]

tests/test_litellm/router_utils/test_health_check_routing.py

@@ -50,6 +50,7 @@ class TestFilterHealthCheckUnhealthyDeployments:
             def __init__(self):
                 self.enable_health_check_routing = enable
                 self.health_state_cache = health_cache
+                self.allowed_fails_policy = None
 
         # Import the actual method and bind it
         from litellm.router import Router
@@ -125,6 +126,7 @@ class TestAsyncFilterHealthCheckUnhealthyDeployments:
             def __init__(self):
                 self.enable_health_check_routing = enable
                 self.health_state_cache = health_cache
+                self.allowed_fails_policy = None
 
         fake = FakeRouter()
         fake._async_filter_health_check_unhealthy_deployments = (