I've decided to write a program that runs into an infinite execution of the method where I was testing (to automate the testing process).

Here's the code snippet I was working with to achieve what Ken White and Frank van Puffelen recommend.

import 'dart:math';

import 'package:flutter/material.dart';
import 'dart:developer' as developer;

class FourDigitCodeGenerator extends StatefulWidget {
  const FourDigitCodeGenerator({super.key});

  @override
  State<FourDigitCodeGenerator> createState() => _FourDigitCodeGeneratorState();
}

class _FourDigitCodeGeneratorState extends State<FourDigitCodeGenerator> {
  String? _code;

  void _generateCode() { // version 1
    Set<int> setOfInts = {};
    var scopedCode = Random().nextInt(9999);
    setOfInts.add(scopedCode);

    for (var num in setOfInts) {
      if (num < 999) return;
      if (num.toString().length == 4) {
        if (mounted) {
          WidgetsBinding.instance.addPostFrameCallback((_) {
            setState(() {
              _code = num.toString();
              developer.log('Code: $num');
            });
          });
        }
      } else {
        if (mounted) {
          WidgetsBinding.instance.addPostFrameCallback((_) {
            setState(() {
              _code = num.toString();
              developer.log('Code: not a 4 digit code');
            });
          });
        }
      }
    }
  }

  void _generateCode2() { // version 2
    Set<int> setOfInts = {};
    var scopedCode = 1000 + Random().nextInt(9000);
    setOfInts.add(scopedCode);

    for (var num in setOfInts) {
      // if (num < 999) return;
      if (num.toString().length == 4) {
        if (mounted) {
          WidgetsBinding.instance.addPostFrameCallback((_) {
            setState(() {
              _code = num.toString();
              developer.log('Code: $num');
            });
          });
        }
      } else {
        if (mounted) {
          WidgetsBinding.instance.addPostFrameCallback((_) {
            setState(() {
              _code = num.toString();
              developer.log('Code: not a 4 digit code');
            });
          });
        }
      }
    }
  }

  @override
  Widget build(BuildContext context) {
    return Builder(builder: (context) {
      _generateCode2();
      return Scaffold(
        appBar: AppBar(
          title: Text('Device ID'),
        ),
        body: Center(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: [
              Text('Code: ${_code ?? 'Nothing to show'}'),
            ],
          ),
        ),
      );
    });
  }
}

Here's the output it provides using version 2 method:

gif

Note: I can't embed a GIF file yet, so it is converted into a link instead (by default).

With the solution provided by Ken White (method version 1) and Frank van Puffelen (method version 2) produces the same outcomes.

So a big thanks to them!

I hope my answer would help the other future readers as well!