How do I send an HTML email using MimeMail module?

There is documentation - see the project page.
There is an example module included with Mime Mail.

All your code samples are wrong. If you still have questions after follow the instructions and looking at the example then ask those specific questions.

I have been unable to find an example of how to send an email formatted as html using mimemail. I do not have a template, and it is my understanding that I do not need a html twig in order to send html emails with mimemail.

I don't see anything helpful in the mimemail_example.module:

/**
 * Implements hook_mail().
 */
function mimemail_example_mail($key, &$message, $params) {
  // The $params array holds the values entered on the ExampleForm, stored
  // with the same structure as the $form array. We need to copy these values
  // to the appropriate place in the $message so that they get used when
  // sending the email.
  $message['from'] = $params['headers']['From'] ?? NULL;

  // Strip newline characters from email subjects.
  $message['subject'] = isset($params['subject']) ? str_replace(["\r\n", "\r", "\n"], ' ', $params['subject']) : NULL;
  $message['body'][] = $params['body'];
}

Forgive me if I do not see any difference between the way you are sending and the way I do it:

$result = $this->mailManager->mail($module, $key, $to, $langcode, $params, $reply, $send);

/**
   * {@inheritdoc}
   */
  public function submitForm(array &$form, FormStateInterface $form_state) {
    // First, assemble arguments for MailManager::mail().
    $module = 'mimemail_example';
    $key = $form_state->getValue('key');
    $to = $form_state->getValue('to');
    $langcode = $this->languageManager->getDefaultLanguage()->getId();
    $params = $form_state->getValue('params');
    $reply = $params['headers']['Reply-to'];
    $send = TRUE;

    // Second, add values to $params and/or modify submitted values.
    // Set From header.
    if (!empty($form_state->getValue('from_mail'))) {
      $params['headers']['From'] = MimeMailFormatHelper::mimeMailAddress([
        'name' => $form_state->getValue('from'),
        'mail' => $form_state->getValue('from_mail'),
      ]);
    }
    elseif (!empty($form_state->getValue('from'))) {
      $params['headers']['From'] = $from = $form_state->getValue('from');
    }
    else {
      // Empty 'from' will result in the default site email being used.
    }

    // Handle empty attachments - we require this to be an array.
    if (empty($params['attachments'])) {
      $params['attachments'] = [];
    }

    // Remove empty values from $param['headers'] - this will force the
    // the formatting mailsystem and the sending mailsystem to use the
    // default values for these elements.
    foreach ($params['headers'] as $header => $value) {
      if (empty($value)) {
        unset($params['headers'][$header]);
      }
    }

    // Finally, call MailManager::mail() to send the mail.
    $result = $this->mailManager->mail($module, $key, $to, $langcode, $params, $reply, $send);
    if ($result['result'] == TRUE) {
      $this->messenger()->addMessage($this->t('Your message has been sent.'));
    }
    else {
      // This condition is also logged to the 'mail' logger channel by the
      // default PhpMail mailsystem.
      $this->messenger()->addError($this->t('There was a problem sending your message and it was not sent.'));
    }
  }

The only thing I can see in the above example is this:

$message['body'][] = $params['body'];

I was NOT sending 'body' as a parameter. So, I modified my code to do so.

So, I changed my sendEmail code to do that:

    $mailManager = \Drupal::service('plugin.manager.mail');
    $module = 'solrai';
    $key = 'notify';
    // $params['message'] = $message;
    $params['body'] = $message;
    $params['subject'] = $subject;

And, in my mail hook:

function solrai_mail($key, &$message, $params) {
  switch ($key) {
    case 'notify':
      $message['body'][] = $params['body']; // HTML content.
      break;
    case 'response':
      // Set the subject and message body.
      $message['subject'] = $params['subject'];
      $message['body'][] = $params['message']; // HTML content.
      break;
  }
}

However, the email output is still plain text. My simple test:

<a href="https://bible.booksai.org/group/3238">How Do I and FAQs</a> | 
<a href="https://bible.booksai.org/support">Contact Support</a>

Still prints out in the email like this:

How Do I and FAQs [1] |
Contact Support [2]

[1] https://bible.booksai.org/group/3238
[2] https://bible.booksai.org/support

The email still looks like this:

So, what part of this process am I missing?

More information.

When I use the Test Mime Mail form and send this code:

Click here for How Do I and FAQs: https://bible.booksai.org/group/3238

Click here to contact Support: https://bible.booksai.org/support

How Do I and FAQs |
Contact Support

I receive this in the email:

Click here for How Do I and FAQs: https://bible.booksai.org/group/3238
Click here to contact Support: https://bible.booksai.org/support
How Do I and FAQs [1] |
Contact Support [2]

[1] https://bible.booksai.org/group/3238
[2] https://bible.booksai.org/support

(null)

So it does look like something else is overriding Mime Mail. How can I discover what this is?

From the project page, https://www.drupal.org/dproject/mimemail →

Quick start

Follow the instructions at https://www.drupal.org/docs/contributed-modules/mime-mail →

Thank you. It appears the problem for me is that I needed to select MimeMail as the email formatter for the module that is sending the emails:

Doing this appears to have resolved the issue. Emails are now being sent in HTML format.

Thank You!

Automatically closed - issue fixed for 2 weeks with no activity.