How does the VIEW ALL DRAFTS blog page get the drafts (if there's no way to get drafts in the API)?

Inactive User, let me know if this approach might work for you.

Try the Community API v1 call for topics/recent. It supports returning messages that are in draft state. The call (using session key authentication) would be:

/restapi/vc/boards/id/<board-id>/topics/recent?visibility.scope=draft&restapi.session_key=<auth-token>

Note that only permissible users are able to see drafts as configured in user permissions for the given node. Furthermore, this will only work for drafts in Blogs and TKBs which are different than the autosave messages available on other interaction styles. 

This REST API endpoint supports the following query parameters and possible values: 

• moderation.scope
  • approved
  • rejected
  • unmoderated
  • marked_undecided
  • marked_approved
  • marked_rejected
  • all_unmoderated
  • mod_private
  • approved_and_all_unmoderated
  • level2_unmoderated
  • moderation_with_reason_code
• visibility.scope
  • public
  • public_moderateable
  • draft
  • on_hold
  • rejected
  • unmoderated
  • marked_undecided
  • marked_approved
  • marked_rejected
  • deleted
  • disabled
  • personal
  • friends_only
  • public_and_draft
  • private
  • not_deleted
  • all
  • none
  • public_and_unmoderated
  • all_moderated
  • mod_private
  • moderator
  • published
• revision.state
  • any
• show_hidden
  • true
  • false