📝 consolidate logger API and async lifecycle guidance

docs/api/async-logger-child.md

@@ -28,16 +28,18 @@ pub fn[S] AsyncLogger::child(self : AsyncLogger[S], target : String) -> AsyncLog
 
 #### output
 
-- `AsyncLogger[S]` - A new async logger whose default target is the composed child path.
+- `AsyncLogger[S]` - A new async logger value whose default target is the composed child path.
 
 ### Explanation
 
 Detailed rules explaining key parameters and behaviors
 
+- The returned logger is derived from `self`; the original async logger value is not mutated.
 - 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 `.`.
-- Queue settings, sink wiring, and runtime behavior are preserved in the returned logger.
+- Only the stored target changes. Queue settings, sink wiring, flush policy, level gating, and lifecycle state remain shared with the same underlying async logger setup.
+- In the current direct async coverage, `timestamp` is also preserved on the derived child logger while the source logger keeps its previous parent target.
 
 ### How to Use
 
@@ -53,6 +55,8 @@ let worker = logger.child("worker")
 
 In this example, `worker` emits under `service.worker` while keeping the same async queue behavior.
 
+And `logger` still keeps its original stored target, because `child(...)` returns a derived async logger value instead of mutating the parent.
+
 #### When Build Deep Async Scopes Step By Step
 
 When deeper target composition should remain readable:
@@ -76,3 +80,7 @@ e.g.:
 1. This is the preferred API for hierarchical async logger naming.
 
 2. Composition changes the target only and does not rebuild the queue or sink.
+
+3. State helpers such as `pending_count()`, `dropped_count()`, `is_closed()`, and `has_failed()` still operate on the same async logger state after derivation.
+
+4. Use `child("")` when code should keep the current target while still following a target-composition code path.