📝 Add async logger composition API docs

docs/api/async-logger-with-target.md

@@ -0,0 +1,78 @@
+---
+name: async-logger-with-target
+group: api
+category: async
+update-time: 20260512
+description: Replace the default target carried by an async logger so later records inherit a new target namespace.
+key-word:
+    - async
+    - logger
+    - target
+    - public
+---
+
+## Async-logger-with-target
+
+Replace the async logger's default target. This API retargets later enqueue operations without changing the queue, overflow policy, or sink wiring.
+
+### Interface
+
+```moonbit
+pub fn[S] AsyncLogger::with_target(self : AsyncLogger[S], target : String) -> AsyncLogger[S] {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Base async logger whose default target should be replaced.
+- `target : String` - New default target namespace.
+
+#### output
+
+- `AsyncLogger[S]` - A new async logger value carrying the updated target.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- The returned logger keeps the same sink, queue state, overflow policy, flush policy, and lifecycle flags.
+- This API replaces the default target instead of composing it.
+- Per-call `target?` arguments on `log(...)` can still override the default target.
+- The original logger value is not mutated.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need A Stable Async Target Namespace
+
+When one async logger should always emit under a fixed target:
+```moonbit
+let logger = async_logger(console_sink())
+  .with_target("service.worker")
+```
+
+In this example, later async log calls inherit `service.worker` unless a call overrides the target explicitly.
+
+#### When Reuse One Async Setup Across Namespaces
+
+When multiple subsystem loggers should share the same async queue behavior:
+```moonbit
+let base = async_logger(console_sink(), config=AsyncLoggerConfig::new(max_pending=64))
+let api = base.with_target("api")
+let jobs = base.with_target("jobs")
+```
+
+In this example, target routing changes without rebuilding the async runtime configuration.
+
+### Error Case
+
+e.g.:
+- If `target` is empty, the logger remains valid and later records default to an empty target.
+
+- If callers need hierarchical target composition rather than replacement, `child(...)` is the better API.
+
+### Notes
+
+1. Use this API for replacement, not parent-child target composition.
+
+2. It is useful when several subsystems should share one async queue policy.