📝 clarify async close post-shutdown log split

docs/api/async-logger-close.md

@@ -40,6 +40,8 @@ Detailed rules explaining key parameters and behaviors
 - This helper does not itself wait for the worker to finish.
 - `close(...)` also does not change `has_failed()` or `last_error()`; it is a closure primitive, not a failure reset API.
 - Because this is a low-level close primitive, it does not first run `wait_idle()` or apply the runtime-dependent fallback logic used by `shutdown()`.
+- After closure, later log attempts do not add new pending or dropped counts, but backend behavior can still differ before the closed queue rejects the record.
+- In the current direct coverage, compatibility runtimes short-circuit before patch-path work on late log attempts, while native-worker runtimes may still build and patch the record before the closed queue rejects it.
 
 ### How to Use
 
@@ -70,6 +72,8 @@ e.g.:
 
 - If `clear=false`, pending records may still exist after closure until worker drain or later cleanup resolves them.
 
+- If callers perform late log attempts after closure, backlog counters still stay unchanged, but patch-path side effects are runtime-dependent and should not be treated as a portable post-close contract.
+
 - If callers need graceful waiting for drain completion, `shutdown()` is usually the better API.
 
 ### Notes