📝 Update More API Document

docs/api/fanout-sink.md

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+---
+name: fanout-sink
+group: api
+category: sink
+update-time: 20260520
+description: Create a sink that writes each record to two sinks.
+key-word:
+    - sink
+    - fanout
+    - routing
+    - public
+---
+
+## Fanout-sink
+
+Create a sink that writes every record to two underlying sinks. This helper is useful when the same log stream should be duplicated across multiple destinations.
+
+### Interface
+
+```moonbit
+pub fn[A, B] fanout_sink(left : A, right : B) -> FanoutSink[A, B] {
+```
+
+#### input
+
+- `left : A` - First sink destination.
+- `right : B` - Second sink destination.
+
+#### output
+
+- `FanoutSink[A, B]` - Sink that duplicates records to both destinations.
+
+### Explanation
+
+Detailed rules explaining key parameters and behaviors
+
+- Each record is written to both sinks.
+- The right side receives a copied record so the two writes remain independent at the record value level.
+- This helper is useful for combinations such as console plus JSON, or console plus callback capture.
+
+### How to Use
+
+Here are some specific examples provided.
+
+#### When Need Dual Output Paths
+
+When the same records should go to both human and machine-oriented outputs:
+```moonbit
+let logger = Logger::new(
+  fanout_sink(console_sink(), json_console_sink()),
+  target="dual",
+)
+```
+
+In this example, each record is written to both console sinks.
+
+### Error Case
+
+e.g.:
+- If only one path should receive a record conditionally, use `split_sink(...)` instead.
+
+- Sink-specific failures still follow the behavior of the wrapped sinks.
+
+### Notes
+
+1. This helper is a duplication primitive, not a conditional router.
+
+2. It is often useful in examples and test capture setups.