[FEATURE] Let agents/skills set the conversation title and file it into a folder/Project

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Agents and skills (Claude Code, Cowork, MCP automations) often run as one conversation per task — a single chat that produces a specific deliverable. The agent knows what the task is, but it has no way to name the conversation or file it into a folder/Project. Naming and foldering a conversation are manual, UI-only actions today.

So every automated run leaves behind an unsorted, auto-titled chat that the user has to rename and sort by hand — repetitive bookkeeping that directly undercuts the automation the skill was built to provide. For anyone who runs the same skill many times, the agent does all the real work and then hands back a "New chat" the human still has to file.

Proposed Solution

Expose a small conversation-management capability to agents/MCP — mirroring how the existing DesignSync tool already lets an agent manage claude.ai projects through the user's login. Minimal surface:

• conversation.set_title(title) — set/rename the current conversation's title.
• conversation.move_to_folder(name, createIfMissing = true) — file the current conversation into a folder/Project by name, creating it if it doesn't exist.
• reads: conversation.get() → { id, title, folder }, and folder.list().

Permissioned like other side-effecting tools (per-action approval, or a one-time "let skills organize my conversations" grant). Idempotent: moving to an existing folder is a no-op; re-titling overwrites.

Alternative Solutions

• mark_chapter (exists today): only labels a section inside one conversation's table of contents — it can't group conversations into a folder or set the conversation title.
• Manual UI: works, but it's exactly the repetitive step the automation should remove, redone on every run.
• Precedent already ships: DesignSync manages claude.ai projects on the user's behalf through their login — the same auth/permission pattern could be reused here.

Priority

Medium - Would be very helpful

Feature Category

MCP server integration

Use Case Example

1. A skill runs a task in its own conversation and produces a deliverable (a report, a record, a ticket response — anything).
2. With this feature, when it finishes it calls move_to_folder("<task name>", createIfMissing=true) then set_title("<descriptive title>").
3. The conversation is filed and named automatically — the user later opens the folder and finds it instantly, instead of scrolling a wall of "New chat" entries.
4. Any "one conversation per task" workflow benefits — reports, tickets, records, research, client work.

Additional Context

• Low surface area, broad payoff for any task-per-conversation workflow.
• Auth model already exists via DesignSync (claude.ai login → manage projects); reuse it rather than inventing a new permission path.
• This is an app feature (claude.ai / Claude Desktop conversation organization) exposed to agents via a tool/MCP — not a model-behavior change, so it's additive and low-risk.