📝 Add async logger lifecycle API docs

docs/api/async-logger-shutdown.md

@@ -0,0 +1,75 @@
+---
+name: async-logger-shutdown
+group: api
+category: async
+update-time: 20260512
+description: Gracefully stop an async logger by waiting for idle or clearing queued work, then waiting for the worker to finish.
+key-word:
+    - async
+    - logger
+    - lifecycle
+    - public
+---
+
+## Async-logger-shutdown
+
+Gracefully stop an async logger. This is the main high-level shutdown API for async logging because it coordinates drain behavior, closure, and worker completion.
+
+### Interface
+
+```moonbit
+pub async fn[S] AsyncLogger::shutdown(self : AsyncLogger[S], clear? : Bool = false) -> Unit {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Async logger that should be shut down.
+- `clear : Bool` - Whether pending records should be abandoned immediately instead of waiting for idle first.
+
+#### output
+
+- `Unit` - No return value. The method completes after shutdown coordination finishes.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- `clear=false` first waits for idle, then closes the logger.
+- If backlog still remains after waiting, shutdown falls back to `close(clear=true)`.
+- `clear=true` immediately closes and abandons pending records.
+- The method waits until `is_running()` becomes `false` before returning.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need Graceful Service Shutdown
+
+When a service should stop logging only after queued records are drained:
+```moonbit
+await logger.shutdown()
+```
+
+In this example, the logger waits for normal drain behavior before final closure.
+
+#### When Need Fast Shutdown Under Pressure
+
+When teardown should prefer speed over preserving backlog:
+```moonbit
+await logger.shutdown(clear=true)
+```
+
+In this example, pending work is abandoned intentionally so shutdown can complete sooner.
+
+### Error Case
+
+e.g.:
+- If `clear=true`, pending records are intentionally dropped rather than drained.
+
+- If callers skip `shutdown()` and only inspect flags manually, it is easier to leave the worker lifecycle in an unclear state.
+
+### Notes
+
+1. Prefer this API over raw `close()` in normal application shutdown paths.
+
+2. Choose `clear=true` only when loss of queued records is acceptable.