📝 consolidate logger API and async lifecycle guidance

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

@@ -2,8 +2,8 @@
 name: library-async-logger-with-target
 group: api
 category: facade
-update-time: 20260613
-description: Replace the default target carried by a LibraryAsyncLogger facade.
+update-time: 20260614
+description: Replace the default target carried by a LibraryAsyncLogger facade while rewrapping the derived async logger state behind the same library-facing surface.
 key-word:
     - async
     - library
@@ -37,10 +37,11 @@ pub fn[S] LibraryAsyncLogger::with_target(
 
 Detailed rules explaining key parameters and behaviors
 
-- This API delegates to the wrapped async logger's `with_target(...)` behavior and then re-wraps the result.
-- The returned value keeps the same queue state, sink type, and async config.
+- This API delegates to the wrapped async logger's `with_target(...)` behavior and then re-wraps the result as another `LibraryAsyncLogger[S]`.
+- The original facade is not mutated. The returned facade stores the replacement target while the source facade keeps its previous target.
+- Timestamp behavior, enabled-level gating, sink type, queue state, async config, and failure/lifecycle state stay the same because only the default target field changes.
 - This replaces the default target instead of composing it.
-- The original facade value is not mutated.
+- Async state helpers remain hidden behind the narrower facade after rewrapping; use `to_async_logger()` if later code needs them.
 
 ### How to Use
 
@@ -70,6 +71,10 @@ let io = base.with_target("io")
 
 In this example, one base facade becomes several target-specific async facades.
 
+And each derived facade still wraps the same kind of queue-backed async logger state, differing only in the default target it carries.
+
+The derived facade keeps the same timestamp and level-gating behavior as the source facade.
+
 ### Error Case
 
 e.g.:
@@ -82,3 +87,5 @@ e.g.:
 1. Use this API for replacement, not target-path composition.
 
 2. It keeps the narrower `LibraryAsyncLogger` boundary intact.
+
+3. Use `child(...)` when the new target should be combined with the current one instead of replacing it.