📝 Add async logger composition API docs

docs/api/async-logger-with-min-level.md

@@ -0,0 +1,80 @@
+---
+name: async-logger-with-min-level
+group: api
+category: async
+update-time: 20260512
+description: Replace the async logger minimum enabled level so lower-severity records are skipped before enqueue.
+key-word:
+    - async
+    - logger
+    - level
+    - public
+---
+
+## Async-logger-with-min-level
+
+Replace the async logger's minimum enabled level. This API controls the first gate checked before record creation and queue insertion.
+
+### Interface
+
+```moonbit
+pub fn[S] AsyncLogger::with_min_level(
+  self : AsyncLogger[S],
+  min_level : @bitlogger.Level,
+) -> AsyncLogger[S] {}
+```
+
+#### input
+
+- `self : AsyncLogger[S]` - Base async logger whose level threshold should change.
+- `min_level : Level` - New minimum enabled level.
+
+#### output
+
+- `AsyncLogger[S]` - A new async logger value carrying the updated threshold.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- `log(...)` checks `is_enabled(level)` before creating a record or touching the queue.
+- Lower-severity records below `min_level` are skipped before enqueue.
+- This API replaces the logger threshold and does not alter queue configuration.
+- The returned logger keeps the same sink, target, and timestamp settings.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Raise Async Noise Floor In Production
+
+When only warning and error records should reach the async queue:
+```moonbit
+let logger = async_logger(console_sink())
+  .with_min_level(@bitlogger.Level::Warn)
+```
+
+In this example, lower-severity records are skipped before queue pressure increases.
+
+#### When Derive A More Verbose Async Branch
+
+When one branch of code should keep a different threshold:
+```moonbit
+let base = async_logger(console_sink(), min_level=@bitlogger.Level::Info)
+let debug_logger = base.with_min_level(@bitlogger.Level::Debug)
+```
+
+In this example, the async sink and queue settings are reused while the threshold changes per logger value.
+
+### Error Case
+
+e.g.:
+- If `min_level` is set too high, expected lower-severity diagnostics may disappear before they ever enter the queue.
+
+- If callers need richer predicate logic than a simple threshold, `with_filter(...)` should be used instead.
+
+### Notes
+
+1. This API reduces async queue pressure by dropping disabled levels before enqueue.
+
+2. Use it before adding more complex async filtering rules.