Sent messages have HTML markup stripped, are plain text

Confirmed. I'm upgrading my own site today, and found that the default PhpMail class in Drupal 8 strips all markup from every message, with no ability to override.

So the quick solution would be to find another mail plugin (like swiftmailer, or mimemail) and set that in your settings.php:

$config['system.mail']['interface']['default'] = 'some_other_system';

I'm going to see if that works. Otherwise you may need to install the mailsystem module to switch. I'm considering adding an interface / plugin to basically do the same thing as core's PhpMail, but removing the part that strips markup from the body.

I've also opened an issue in my site's issue tracker to see if I can come up with a temporary solution: Emails are not sent with HTML formatting.

I just noticed I implement a mail handler: SimpleMailMailer. It looks like the file is named incorrectly so it can't be identified / used currently.

But if it could be and if I could get it to work with HTML emails, you could override in settings.php:

$config['system.mail']['interface']['default'] = 'simple_mail_mailer';

If I try the above I get:

In DiscoveryTrait.php line 53:
                                                                                                                       
  The "simple_mail_mailer" plugin does not exist. Valid plugin IDs for Drupal\Core\Mail\MailManager are: php_mail, test_mail_collector 

Attached patch fixes the HTML email problem.

To use the SimpleMail plugin, you have to add the following to your settings.php:

$config['system.mail']['interface']['default'] = 'simple_mail';

Also opened up follow-up issue: #3159949: No plain-text alternative is delivered when using simple_mail_send().