Expand Engagement Inbox to Support Native Social Media DMs

What problem does this solve
Currently, Mixpost’s Engagement module successfully centralizes public interactions (comments and mentions), but it completely misses private interactions. Customer support and community management often happen behind closed doors in Direct Messages (DMs).

Because Mixpost does not support DMs, social media managers are forced to constantly context-switch. We have to use Mixpost for publishing and public comments, but then log into native apps (like Facebook Business Suite, Instagram, and X) to handle private customer inquiries. This fragments our workflow, increases response times, and prevents teams from collaborating efficiently on private support tickets within a single self-hosted dashboard.

Describe the solution
Expand the existing Engagement Inbox to act as a fully unified social inbox by adding Direct Message capabilities.

API Integration: Integrate with the private messaging endpoints of the supported networks (e.g., Meta’s pages_messaging and instagram_manage_messages permissions, and X's DM API).

Inbox UI: Add a "Messages" or "DMs" filter alongside the current "Comments" and "Mentions" tabs in the UI so users can easily distinguish private threads from public replies.

Real-time sync: Utilize webhooks to pull in DMs in real-time and allow users to type and send replies back to the user directly from the Mixpost interface.