[pigeon] Separates message call code generation into separate methods in the DartGenerator (#5859)

Separates message call code generation into separate methods in the  `DartGenerator` for flutter/flutter#134777. The `ProxyApi` generator uses similar code to the `HostApi` and `FlutterApi`, so this makes the code reusable.

Separated from #5544

From suggestion: #5544 (comment)

Author: bparrishMines

packages/pigeon/CHANGELOG.md

@@ -1,3 +1,7 @@
+## 16.0.2
+
+* [dart] Separates message call code generation into separate methods.
+
 ## 16.0.1
 
 * [dart] Fixes test generation for missing wrapResponse method if only host Api.