📝 Add async logger write API docs

docs/api/async-logger-error.md

@@ -0,0 +1,83 @@
+---
+name: async-logger-error
+group: api
+category: async
+update-time: 20260512
+description: Enqueue an error-level record through the async logger using the highest built-in severity shortcut.
+key-word:
+    - async
+    - logger
+    - error
+    - public
+---
+
+## Async-logger-error
+
+Enqueue an error-level record through the async logger. This is the convenience wrapper for `log(Level::Error, ...)`.
+
+### Interface
+
+```moonbit
+pub async fn[S] AsyncLogger::error(
+  self : AsyncLogger[S],
+  message : String,
+  fields~ : Array[@bitlogger.Field] = [],
+) -> Unit {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Async logger that should receive the error record.
+- `message : String` - Error message text.
+- `fields : Array[Field]` - Optional structured fields added to the record.
+
+#### output
+
+- `Unit` - No return value. The record is handled according to logger state and policy.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- This helper delegates to `log(Level::Error, ...)`.
+- The record is still subject to patching, filtering, and overflow policy.
+- Error records represent the highest built-in severity in this logger API.
+- Use this helper when a named error call is clearer than a raw `log(...)` call.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need Async Failure Reporting
+
+When an operation should emit a high-severity failure event:
+```moonbit
+await logger.error("worker execution failed")
+```
+
+In this example, failure intent is explicit at the call site.
+
+#### When Attach Structured Error Context
+
+When an error event should include diagnostic fields:
+```moonbit
+await logger.error(
+  "dispatch failed",
+  fields=[@bitlogger.field("job_id", "42")],
+)
+```
+
+In this example, the error record carries structured context without falling back to the generic `log(...)` form.
+
+### Error Case
+
+e.g.:
+- If the logger is closed or overflow policy prevents acceptance, even an error-level record may not become a normal queued record.
+
+- If callers need to inspect worker failure rather than emit an error record, `has_failed()` and `last_error()` are the relevant APIs.
+
+### Notes
+
+1. Use this helper for high-severity async application failures.
+
+2. Emitting an error record is separate from the logger worker itself entering failure state.