Contact Form: Set message content type to restore compat with plugins

[iandunn]

Some plugins override wp_mail() and replace PHPMailer with other libraries, like Zend Mail. Previously, we were relying on PHPMailer to correctly set the content type, but that never happens when other libraries are used. Because of that, the message can be sent out with a text/plain type, but contain HTML, making it difficult for users to read.

All plugins should respect the value of wp_mail_content_type, though, so this is a much more reliable method of setting the type to text/html.

Props georgestephanis, jeherve
Fixes #7003

Testing instructions:

1. Install the Postman SMTP or Gmail SMTP plugins from the w.org repo
2. Checkout master, and submit a contact form. You'll see the raw HTML because the content-type is text/plain
3. Checkout this branch and repeat the test. It should display in HTML and have the content-type set to text/html

[dereksmart]

Works well! just needs a rebase to fix conflicts :)

[dereksmart]

Fixed the conflicts -- this should be good to go!

[iandunn]

Thanks Derek, that was on my list for today but you beat me to it :)

[eliorivero]

Looks good!