📝 consolidate logger API and async lifecycle guidance

docs/api/library-logger-child.md

@@ -3,7 +3,7 @@ name: library-logger-child
 group: api
 category: facade
 update-time: 20260613
-description: Derive a child LibraryLogger facade by composing the current target with a child segment.
+description: Derive a child LibraryLogger facade by composing the current target with a child segment while rewrapping the same underlying logger state.
 key-word:
     - library
     - facade
@@ -38,6 +38,8 @@ Detailed rules explaining key parameters and behaviors
 - If the parent target is empty, the child target becomes the full target.
 - If the child target is empty, the parent target is preserved.
 - If both are non-empty, they are joined with `.`.
+- Sink type, minimum level, timestamp behavior, and any existing sink wrappers remain the same because only the derived target changes.
+- Broader composition helpers remain hidden behind the narrower facade after rewrapping; use `to_logger()` if later code needs them.
 
 ### How to Use
 
@@ -65,6 +67,8 @@ let client = LibraryLogger::new(console_sink(), target="sdk")
 
 In this example, the final facade emits under `sdk.http.client`.
 
+And the target derivation does not rebuild or reset the wrapped logger pipeline.
+
 ### Error Case
 
 e.g.:
@@ -77,3 +81,5 @@ e.g.:
 1. This is the preferred library-facing API for hierarchical target naming.
 
 2. Composition uses `.` as the separator between parent and child segments.
+
+3. Use `with_target(...)` instead when the new target should replace the current target rather than extend it.