📝 align async lifecycle examples

docs/api/async-logger-shutdown.md

@@ -47,7 +47,7 @@ Here are some specific examples provided.
 
 When a service should stop logging only after queued records are drained:
 ```moonbit
-await logger.shutdown()
+logger.shutdown()
 ```
 
 In this example, the logger waits for normal drain behavior before final closure.
@@ -56,7 +56,7 @@ In this example, the logger waits for normal drain behavior before final closure
 
 When teardown should prefer speed over preserving backlog:
 ```moonbit
-await logger.shutdown(clear=true)
+logger.shutdown(clear=true)
 ```
 
 In this example, pending work is abandoned intentionally so shutdown can complete sooner.

docs/api/async-logger-wait-idle.md

@@ -2,8 +2,8 @@
 name: async-logger-wait-idle
 group: api
 category: async
-update-time: 20260512
-description: Wait until the async logger backlog drains to zero or a worker failure interrupts normal progress.
+update-time: 20260614
+description: Wait until the async logger backlog drains to zero or a worker failure interrupts normal progress, using the repo's direct async call style.
 key-word:
     - async
     - logger
@@ -46,7 +46,7 @@ Here are some specific examples provided.
 
 When code should wait for queued work to flush before continuing:
 ```moonbit
-await logger.wait_idle()
+logger.wait_idle()
 ```
 
 In this example, the caller waits for backlog drain but leaves the logger usable afterward.
@@ -55,7 +55,7 @@ In this example, the caller waits for backlog drain but leaves the logger usable
 
 When a test wants to ensure earlier async logs were processed:
 ```moonbit
-await logger.wait_idle()
+logger.wait_idle()
 println("phase complete")
 ```
 

docs/api/library-async-logger-shutdown.md

@@ -51,7 +51,7 @@ Here are some specific examples provided.
 
 When a service should stop logging only after queued records are drained:
 ```moonbit
-await logger.shutdown()
+logger.shutdown()
 ```
 
 In this example, the facade waits for normal drain behavior before final closure.
@@ -60,7 +60,7 @@ In this example, the facade waits for normal drain behavior before final closure
 
 When teardown should prefer speed over preserving backlog:
 ```moonbit
-await logger.shutdown(clear=true)
+logger.shutdown(clear=true)
 ```
 
 In this example, pending work is abandoned intentionally so shutdown can complete sooner.