controllers/test/routes/web.php

<?php

use Illuminate\Support\Facades\Route;
use App\Http\Controllers\HomeController;
use App\Http\Controllers\Auth\RegisterController;
use App\Http\Controllers\Auth\LoginController;

Route::get('/', function () {
    return view('welcome');
});

Auth::routes();

Route::get('/home', [HomeController::class, 'index'])->name('home');

Route::get('/register', [RegisterController::class, 'showRegistrationForm'])->name('register');
Route::post('/register', [RegisterController::class, 'register']);

Route::get('/login', [LoginController::class, 'showLoginForm'])->name('login');
Route::post('/login', [LoginController::class, 'login']);
Route::post('/logout', [LoginController::class, 'logout'])->name('logout');

This concludes a fully working implementation.