Mailgun API failing silently in Laravel 8.54

I've been trying for a full day to understand why my attempt to send mail with the Mailgun API fails silently in my Laravel 8 project. I know there are other questions here with a similar complaint, but so far none of the answers to these other questions have helped.

One potential clue is that when I comment out the mailgun domain and secret in my .env file, I get no errors. But I can't determine why.

I am using the free sandbox domain with the US location.

Here are my env variables:

MAIL_MAILER=mailgun
MAIL_HOST=smtp.mailgun.org
MAIL_PORT=587
MAIL_USERNAME=null
MAIL_PASSWORD=null
MAIL_ENCRYPTION=null
MAIL_FROM_NAME="${APP_NAME}"
MAILGUN_DOMAIN=https://api.mailgun.net/v3/....mailgun.org
MAILGUN_SECRET=5...9

services.php:

<?php

return [

    /*
    |--------------------------------------------------------------------------
    | Third Party Services
    |--------------------------------------------------------------------------
    |
    | This file is for storing the credentials for third party services such
    | as Mailgun, Postmark, AWS and more. This file provides the de facto
    | location for this type of information, allowing packages to have
    | a conventional file to locate the various service credentials.
    |
    */

    'mailgun' => [
        'domain' => env('MAILGUN_DOMAIN'),
        'secret' => env('MAILGUN_SECRET'),
    ],

    'postmark' => [
        'token' => env('POSTMARK_TOKEN'),
    ],

    'ses' => [
        'key' => env('AWS_ACCESS_KEY_ID'),
        'secret' => env('AWS_SECRET_ACCESS_KEY'),
        'region' => env('AWS_DEFAULT_REGION', 'us-east-1'),
    ],

];

mail.php:

<?php

return [

    /*
    |--------------------------------------------------------------------------
    | Default Mailer
    |--------------------------------------------------------------------------
    |
    | This option controls the default mailer that is used to send any email
    | messages sent by your application. Alternative mailers may be setup
    | and used as needed; however, this mailer will be used by default.
    |
    */

    'default' => env('MAIL_MAILER', 'mailgun'),

    /*
    |--------------------------------------------------------------------------
    | Mailer Configurations
    |--------------------------------------------------------------------------
    |
    | Here you may configure all of the mailers used by your application plus
    | their respective settings. Several examples have been configured for
    | you and you are free to add your own as your application requires.
    |
    | Laravel supports a variety of mail "transport" drivers to be used while
    | sending an e-mail. You will specify which one you are using for your
    | mailers below. You are free to add additional mailers as required.
    |
    | Supported: "smtp", "sendmail", "mailgun", "ses",
    |            "postmark", "log", "array"
    |
    */

...

ExampleMail.php:

<?php

namespace App\Mail;

use Illuminate\Bus\Queueable;
use Illuminate\Contracts\Queue\ShouldQueue;
use Illuminate\Mail\Mailable;
use Illuminate\Queue\SerializesModels;

class ExampleMail extends Mailable
{
    use Queueable, SerializesModels;

    /**
     * Create a new message instance.
     *
     * @return void
     */
    public function __construct()
    {
        //
    }

    /**
     * Build the message.
     *
     * @return $this
     */
    public function build()
    {
        return $this
            ->from('no-reply@example.com')
            ->markdown('emails.example');
    }
}

And in my controller, I am doing the following:

Mail::to('[my hard-coded email]')->send(new ExampleMail());

Can anyone help me spot the problem? I have guzzle installed: "guzzlehttp/guzzle": "^7.4", so this shouldn't be the issue and even if it was, there would be at least some kind of error.

Help would be greatly appreciated. I am still pretty new to Laravel so I'm currently in over my head.