📝 Add async logger lifecycle API docs

docs/api/async-logger-close.md

@@ -0,0 +1,75 @@
+---
+name: async-logger-close
+group: api
+category: async
+update-time: 20260512
+description: Close the async logger queue and optionally clear pending records immediately.
+key-word:
+    - async
+    - logger
+    - lifecycle
+    - public
+---
+
+## Async-logger-close
+
+Close the async logger queue and stop treating the logger as an active enqueue target. This API is the low-level lifecycle close primitive behind shutdown flows.
+
+### Interface
+
+```moonbit
+pub fn[S] AsyncLogger::close(self : AsyncLogger[S], clear? : Bool = false) -> Unit {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Async logger that should be closed.
+- `clear : Bool` - Whether pending records should be abandoned immediately instead of being left for drain behavior.
+
+#### output
+
+- `Unit` - No return value. The logger lifecycle state is updated in place.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- `close(...)` marks the logger as closed immediately.
+- `clear=false` closes the queue without explicitly abandoning pending records in the helper itself.
+- `clear=true` counts pending records as dropped and resets `pending_count` to `0` before closing the queue.
+- This helper does not itself wait for the worker to finish.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need Immediate Queue Closure
+
+When teardown should stop normal enqueue activity right away:
+```moonbit
+logger.close()
+```
+
+In this example, the logger enters closed state immediately.
+
+#### When Need To Abandon Backlog Explicitly
+
+When pending records should be discarded during fast shutdown:
+```moonbit
+logger.close(clear=true)
+```
+
+In this example, queued backlog is counted as dropped instead of waiting for further drain.
+
+### Error Case
+
+e.g.:
+- If `clear=true`, pending records are intentionally discarded and contribute to `dropped_count()`.
+
+- If callers need graceful waiting for drain completion, `shutdown()` is usually the better API.
+
+### Notes
+
+1. This is a low-level lifecycle helper; prefer `shutdown()` for normal graceful teardown.
+
+2. Use `clear=true` only when backlog loss is an acceptable shutdown tradeoff.