docs(proxy): describe the health-check routing startup window

Until the first background cycle finishes, every deployment is treated
as healthy. A lower model_info.health_check_timeout shortens that window.

docs/proxy/health_check_routing.md

@@ -0,0 +1,9 @@
+# Health check driven routing
+
+## Startup behavior
+
+Until the first background cycle completes, every deployment is treated as healthy. A request in that window can still be sent to a deployment that is already down, and it waits for that deployment's request timeout before falling back.
+
+The cycle writes those results only after its probes finish. Each probe waits up to `model_info.health_check_timeout` seconds, or `HEALTH_CHECK_TIMEOUT_SECONDS` when that field is unset (60 seconds by default, overridable with the `HEALTH_CHECK_TIMEOUT_SECONDS` environment variable). A lower `model_info.health_check_timeout` shortens this window.
+
+When `allowed_fails_policy` is set and `background_health_check_model_groups` is not, cooldown is what removes a deployment. That counter is also empty until the first cycle records a failure, so the same window applies.