📝 Add async logger lifecycle API docs

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

@@ -0,0 +1,76 @@
+---
+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.
+key-word:
+    - async
+    - logger
+    - failure
+    - public
+---
+
+## Async-logger-has-failed
+
+Read whether the async logger worker has encountered a failure. This helper is a compact health signal for async delivery problems.
+
+### Interface
+
+```moonbit
+pub fn[S] AsyncLogger::has_failed(self : AsyncLogger[S]) -> Bool {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Async logger whose failure flag should be inspected.
+
+#### output
+
+- `Bool` - Whether the worker has failed.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- `run()` clears previous failure state at startup.
+- 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.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need A Fast Failure Signal
+
+When runtime diagnostics should branch on worker health:
+```moonbit
+if logger.has_failed() {
+  println(logger.last_error())
+}
+```
+
+In this example, the code checks failure state first, then reads the error detail.
+
+#### When Inspect Async Runtime State In Tests
+
+When a test needs to confirm that drain execution stayed healthy:
+```moonbit
+ignore(logger.has_failed())
+```
+
+In this example, the helper exposes a simple pass-fail runtime indicator.
+
+### Error Case
+
+e.g.:
+- If `has_failed()` is `false`, queue pressure or dropped records may still exist for non-failure reasons.
+
+- If `has_failed()` is `true`, callers should inspect `last_error()` or `state()` for more context.
+
+### Notes
+
+1. This helper reports worker failure, not general queue stress.
+
+2. Pair it with `last_error()` when you need actionable detail.