Avoid analyzing API example code twice, clean-up (#103548)

Author: goderbauer

dev/bots/analyze.dart

@@ -171,10 +171,10 @@ Future<void> run(List<String> arguments) async {
     ...arguments,
   ]);
 
-  // Analyze all the sample code in the repo.
-  print('$clock Sample code...');
+  // Analyze the code in `{@tool snippet}` sections in the repo.
+  print('$clock Snippet code...');
   await runCommand(dart,
-    <String>[path.join(flutterRoot, 'dev', 'bots', 'analyze_sample_code.dart'), '--verbose'],
+    <String>[path.join(flutterRoot, 'dev', 'bots', 'analyze_snippet_code.dart'), '--verbose'],
     workingDirectory: flutterRoot,
   );