The "unread indicator" next to [My Inbox], [Collaborations], or [Mentioned] will only be visible when the user is assigned as the Contact owner, collaborator, or is mentioned in an internal note within the conversation.

As a team admin who is neither the Contact owner nor a collaborator, the user will not see the unread indicator next to these columns; it will only appear in the conversation preview list.

Suggest adding the "unread indicator" display next to each team inbox next to [Company inbox], so that team admin users will be notified whenever there is a new incoming message from the team's perspective.