Can use the route found in api.php in another file in the routes directory laravel 11?

Question

I need to localize the API web application, especially the auth pages in the lang directory but I have a problem with how to use the route in auth.php instead of api.php in the routes directory.

Note that I used breeze package.

middleware -> SetAppLang.php

public function handle(Request $request, Closure $next): Response
{
    if (! in_array($request->segments(1), config('app.available_locales'))) {

        abort(404);
    }

    App::setLocale($request->segments(1));
    return $next($request);

}

bootstrap\app.php

'languages'=>App\Http\Middleware\SetAppLang::class,

config\app.php

'available_locales' => [
    'en',
    'ar'
],

routes\auth.php

Route::middleware(['auth','languages'])->prefix('{locale}')->group(function () {
    Route::get('verify-email', EmailVerificationPromptController::class)
                ->name('verification.notice');
.
.
.
});

I tried using middleware in api.php but I failed, can anyone help?