Helpdesk — The queue
The inbox shows conversations, not a folder of everything open. Its default is waiting on a reply — the ones where the customer spoke last — which is a different and much shorter list than “open”.
The whole conversation lives on the record: both directions in one ordered list, with the channel each message came through. A note to a colleague is a different kind of thing from a reply, and structurally so — who may read a message is recorded separately from who wrote it, so an internal note cannot reach the customer by accident.
Your existing columns are detected, never invented. Opening the inbox does not add an “Assignee” or a “Status” column to somebody’s table; it finds the ones already there, and offers an explicit button when there are none.
One queue for every way a customer can reach you — the conversation in the middle, and the record it belongs to on the right.