How to test response to failed notification?

I want to be able to alert my application admins if a notification fails to send. Typically this happens using Postmark when the email address is marked by Postmark as inactive and this exception is thrown Symfony\Component\Mailer\Exception\HttpTransportException: Unable to send an email: You tried to send to a recipient that has been marked as inactive.

I've been trying to do it by adding the Trait below to the notification to provide a common failed() method which sends a different FailedNotification to the admins. I also use it to set a common via method so that I can pass the failed notifiable (User) to to the notification that will go to the admin.

namespace App\Traits\User;

use App\Models\User;
use App\Notifications\Admin\FailedNotification;
use Throwable;

trait NotificationFailed
{
    public User $notifiable;

    public function via(User $user) : array
    {
        $this->notifiable = $user;

        return ['mail'];
    }

    public function failed(Throwable $exception) : void
    {
        User::role('administrator')
            ->get()
            ->each(fn ($user) => $user->notify(new FailedNotification($exception, $this->notifiable)));
    }
}

The HttpTransportException doesn't get caught and processed as far as I can see. I'd like to know why so I've been scratching my head about how to test it properly (which would be a good thing anyway).

I can't find a way to set things up so that Notification::fake() in my test results in the HttpTransportException being thrown so I can see what happens.

I'd be grateful for any suggestions :)