📝 refine async failure helper docs

docs/api/async-logger-has-failed.md

@@ -2,8 +2,8 @@
 name: async-logger-has-failed
 group: api
 category: async
-update-time: 20260512
-description: Read whether the async logger worker has encountered a failure during queue drain.
+update-time: 20260614
+description: Read whether the async logger worker has recorded a runtime failure after run() startup reset and drain execution.
 key-word:
     - async
     - logger
@@ -34,6 +34,7 @@ pub fn[S] AsyncLogger::has_failed(self : AsyncLogger[S]) -> Bool {}
 Detailed rules explaining key parameters and behaviors
 
 - `run()` clears previous failure state at startup.
+- `run()` also clears the stored `last_error()` string at startup before drain work begins.
 - If the worker loop raises an error, the logger records that failure and exposes it through this flag.
 - This helper is intentionally compact and should usually be paired with `last_error()` for details.
 - Failure state is about runtime drain execution, not whether records were dropped due to overflow policy.
@@ -67,6 +68,8 @@ In this example, the helper exposes a simple pass-fail runtime indicator.
 e.g.:
 - If `has_failed()` is `false`, queue pressure or dropped records may still exist for non-failure reasons.
 
+- If `has_failed()` becomes `true`, `wait_idle()` may stop early while pending records still remain until a later close or clear path handles them.
+
 - If `has_failed()` is `true`, callers should inspect `last_error()` or `state()` for more context.
 
 ### Notes
@@ -74,3 +77,5 @@ e.g.:
 1. This helper reports worker failure, not general queue stress.
 
 2. Pair it with `last_error()` when you need actionable detail.
+
+3. Pair it with `is_running()` or `state()` when you also need to know whether the worker has already exited and whether backlog remains.