We did just launch the Premium tier of the Account Activity API!
The Premium and Enterprise versions of the Account Activity API do include Direct Messages, as well as several other activities. You can see a list of these activities, as well as the differences in the number of unique subscriptions allowed with each tier of product here: https://developer.twitter.com/en/docs/accounts-and-users/subscribe-account-activity/overview
If you navigate to your Developer Environments page through your developer account, you should either already have an Account Activity API environment already set up, or should be able to set up a new one to get access to the Sandbox product tier.
The Enterprise and Premium endpoints are different. Please refer to our API Reference page to learn more.
Please review our FAQs, and let me know if you have any other questions.