📝 clarify sync level threshold derivation

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

@@ -36,8 +36,9 @@ Detailed rules explaining key parameters and behaviors
 
 - `log(...)` checks `is_enabled(level)` before constructing and writing a record.
 - Lower-severity records below `min_level` are skipped without reaching the sink.
-- This API replaces the logger threshold and does not add a wrapper sink.
-- The returned logger keeps the same sink, target, and timestamp settings.
+- The returned logger is derived from `self`; the original logger value is not mutated.
+- This API replaces the stored threshold and does not add a wrapper sink.
+- Only `min_level` changes. Sink, target, and timestamp behavior stay on the same `Logger[S]` surface.
 
 ### How to Use
 
@@ -53,6 +54,8 @@ let logger = Logger::new(console_sink())
 
 In this example, `trace`, `debug`, and `info` calls are skipped.
 
+The returned logger still uses the same ordinary synchronous logging calls; only the severity gate changes.
+
 #### When Derive A More Verbose Local Logger
 
 When one branch of code should keep a different threshold:
@@ -70,3 +73,11 @@ e.g.:
 
 - If callers need richer predicate logic than a simple threshold, `with_filter(...)` should be used instead.
 
+### Notes
+
+1. This API skips disabled levels before any sink write happens.
+
+2. Use it before adding more complex predicate-based filtering rules.
+
+3. Use a derived logger value when one branch should tighten the threshold and the base logger should keep its broader level gate.
+