📝 align remaining async examples

docs/api/async-logger-debug.md

@@ -2,8 +2,8 @@
 name: async-logger-debug
 group: api
 category: async
-update-time: 20260512
-description: Enqueue a debug-level record through the async logger using the built-in severity shortcut.
+update-time: 20260614
+description: Enqueue a debug-level record through the async logger using the built-in severity shortcut and the repo's direct async call style.
 key-word:
     - async
     - logger
@@ -52,7 +52,7 @@ Here are some specific examples provided.
 
 When intermediate async flow details should be visible during debugging:
 ```moonbit
-await logger.debug("loaded worker config")
+logger.debug("loaded worker config")
 ```
 
 In this example, the call site communicates its intended diagnostic level directly.
@@ -61,7 +61,7 @@ In this example, the call site communicates its intended diagnostic level direct
 
 When a debug event should include extra fields:
 ```moonbit
-await logger.debug(
+logger.debug(
   "dispatch start",
   fields=[@bitlogger.field("job_id", "42")],
 )

docs/api/async-logger-trace.md

@@ -2,8 +2,8 @@
 name: async-logger-trace
 group: api
 category: async
-update-time: 20260512
-description: Enqueue a trace-level record through the async logger using the lowest built-in severity shortcut.
+update-time: 20260614
+description: Enqueue a trace-level record through the async logger using the lowest built-in severity shortcut and the repo's direct async call style.
 key-word:
     - async
     - logger
@@ -52,7 +52,7 @@ Here are some specific examples provided.
 
 When low-level execution flow should be observable during debugging:
 ```moonbit
-await logger.trace("entered reconciliation step")
+logger.trace("entered reconciliation step")
 ```
 
 In this example, the call site makes trace intent explicit.
@@ -61,7 +61,7 @@ In this example, the call site makes trace intent explicit.
 
 When a trace event should carry extra fields:
 ```moonbit
-await logger.trace(
+logger.trace(
   "cache probe",
   fields=[@bitlogger.field("key", "user:42")],
 )

docs/api/library-async-logger-is-enabled.md

@@ -2,8 +2,8 @@
 name: library-async-logger-is-enabled
 group: api
 category: facade
-update-time: 20260613
-description: Check whether a LibraryAsyncLogger facade would accept a record at a given level.
+update-time: 20260614
+description: Check whether a LibraryAsyncLogger facade would accept a record at a given level before using the repo's direct async call style.
 key-word:
     - async
     - library
@@ -51,7 +51,7 @@ Here are some specific examples provided.
 When debug data should only be built if needed:
 ```moonbit
 if logger.is_enabled(@bitlogger.Level::Info) {
-  await logger.info(build_summary())
+  logger.info(build_summary())
 }
 ```
 
@@ -62,7 +62,7 @@ In this example, expensive preparation is skipped unless the current threshold a
 When package code should branch based on current logger behavior:
 ```moonbit
 if logger.is_enabled(@bitlogger.Level::Warn) {
-  await logger.warn("slow path active")
+  logger.warn("slow path active")
 }
 ```