How to auth user via WP-API?

Hello,

I write an function to login a user from his ID via WP-API:

public function login(WP_REST_Request $request)
{
$user_id = $request->get_param('user_id');

    if ($user_id) {
        $user = get_user_by('id', $user_id);

        if ($user) {
            wp_set_current_user($user->ID);
            wp_set_auth_cookie($user->ID, true);

            return new WP_REST_Response(true, 200);
        } else {
            return new WP_Error('user-not-found', 'User not found', ['status' => 500]);
        }
    } else {
        return new WP_Error('user-id-not-found', 'User id not found', ['status' => 500]);
    }
}

But when I go back to website, user is not logged, no cookies are set 🙁

How can I do this ?

Thanks!

https://wordpress.org/plugins/json-rest-api/