📝 Add async logger lifecycle API docs

docs/api/async-logger-wait-idle.md

@@ -0,0 +1,75 @@
+---
+name: async-logger-wait-idle
+group: api
+category: async
+update-time: 20260512
+description: Wait until the async logger backlog drains to zero or a worker failure interrupts normal progress.
+key-word:
+    - async
+    - logger
+    - queue
+    - public
+---
+
+## Async-logger-wait-idle
+
+Wait until the async logger backlog drains to zero. This helper is useful when callers want to observe idle state without fully shutting down the logger.
+
+### Interface
+
+```moonbit
+pub async fn[S] AsyncLogger::wait_idle(self : AsyncLogger[S]) -> Unit {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Async logger whose backlog should be waited on.
+
+#### output
+
+- `Unit` - No return value. The method completes when the logger becomes idle or failure prevents normal progress.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- The helper keeps yielding while `pending_count() > 0`.
+- If `has_failed()` becomes `true`, waiting stops early instead of looping forever.
+- This API does not close the logger or stop the worker.
+- It is narrower than `shutdown()` and is useful when the logger should continue to be used later.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need A Drain Barrier Without Shutdown
+
+When code should wait for queued work to flush before continuing:
+```moonbit
+await logger.wait_idle()
+```
+
+In this example, the caller waits for backlog drain but leaves the logger usable afterward.
+
+#### When Need Phase Boundaries In Tests
+
+When a test wants to ensure earlier async logs were processed:
+```moonbit
+await logger.wait_idle()
+println("phase complete")
+```
+
+In this example, the wait acts as a barrier between test phases.
+
+### Error Case
+
+e.g.:
+- If the worker has failed, `wait_idle()` stops waiting even if pending records remain.
+
+- If the worker was never started, pending records may not drain and callers should not expect idle progress automatically.
+
+### Notes
+
+1. Use this helper when you want a drain barrier without closing the logger.
+
+2. Prefer `shutdown()` when lifecycle completion matters more than continued reuse.