Dart code generator: Find class construction and analyze method calls

Question

I want to craft a code generator that analyzes the following code:

void main() {
  @GenerateCode()
  final myClass = MyClass();
  myClass.method1('test', ...);
}

My objective is to extract each construction of MyClass and all the method1 calls with its parameters on that specific construction. I succeed with finding the main function, but can't succeed in finding the variable myClass or the construction of MyClass respectively. I assumed that the .children on the FunctionElement for main would provide me with, among others, the final myClass = MyClass(); line of some sort, but the list is always empty.

Therefor I have two problems:

1. How do I find the construction of MyClass inside the main function?
2. Assuming the construction of MyClass was found, how can I list all the method1 calls in the code base, that reference this instance of MyClass since there could be multiple constructions of MyClass?

This is my debug-approach using a ResursiveElementVisitor. While I can find the main function, no children are accessible.

import 'dart:async';

import 'package:analyzer/dart/element/element.dart';
import 'package:analyzer/dart/element/visitor.dart';
import 'package:build/build.dart';
import 'package:source_gen/source_gen.dart';

Builder copyBuilder(BuilderOptions options) =>
    SharedPartBuilder([MyBuilder()], 'my_builder');

class MyVisitor extends RecursiveElementVisitor {
  @override
  visitFunctionElement(FunctionElement element) {
    print(element.children); // this is an empty list
    super.visitFunctionElement(element);
  }
}

class MyBuilder implements Generator {
  @override
  FutureOr<String?> generate(
      LibraryReader libraryReader, BuildStep buildStep) async {
    libraryReader.element.visitChildren(MyVisitor());

    return '';
  }
}