How to set filtering in vue template with models listing?

Question

With laravel 9/Inertiajs3 I have crud defined with route

Route::resource('models', ModelController::class)->except(['show']);

and main crud methods in control. I wonder in which way can I to set filtering by some field, like having condition in control :

public function index($filter_name = '')
{
    $models= Model
        ::getByName($filter_name)
        ->paginate(5);
    return Inertia::render('Admins/Models/Index', [
        'models'       => $models,
    ]);
}

I suppose I need to add in routes like :

Route::post('models-filter', 'API\Admin\ModelController@index');

But how can I send POST request from vue template with models listing, which has no form defined ?

Thanks in advance!