Add a feature where assigned conversations become visible only to the assigned agent, similar to CRM lead ownership.

Current issue:

All team members can see and reply to all conversations, even after assignment.

This causes multiple replies on the same chat and no clear ownership.

Requested behavior:

Once a conversation is assigned:

Only the assigned agent can see and reply

Other agents cannot access it

Admins/supervisors still have full visibility

Agent name should be attached to the conversation for CRM syncing

Goal:

Prevent duplicate replies, enforce ownership, and align Inbox with CRM workflow.