Show and edit each agent's project association #3

Problem

The Agents sidebar shows agent names, but their associated projects are not clear at a glance. When several agents have custom names, users must open them to understand which project each one belongs to.

Requested behavior

Show each project agent's associated project alongside its identity in the Agents sidebar. Keep the agent name primary and make the project association readable without opening the chat or relying on a tooltip. Distinguish the main agent's cross-project role.

Keep the presentation compact and consistent with the existing sidebar. Project names should also work for business and other non-coding workspaces. When multiple environments are connected, retain enough context to distinguish similarly named projects.

Acceptance criteria

• Users can identify an agent's associated project directly from the sidebar.
• Custom agent names remain visible and distinct from project names.
• The main agent is clearly identified as working across projects.
• Long names remain usable within the sidebar width.
• Project association remains correct after renaming an agent or project.
• Delegated task threads remain separate from agent entries.

The user expanded this issue to allow assigning or changing a project agent's project from its editor and through the main agent. Keep the agent name styling unchanged and make the secondary project label smaller.

Reassignment must preserve agent identity and leave old conversations/tasks in their original projects. Start a fresh conversation in the destination, clear project-specific memory with an explicit explanation, reject occupied destinations and active work, and keep the main agent cross-project. Expose assignment in web/desktop and mobile settings. Main-agent tools may reassign project agents; project agents must not move themselves through tools.