Support `/rename` in VS Code agent sessions, and let the agent invoke it

## Problem

`/rename` (added in #1776) works in the terminal CLI, but not for Copilot CLI sessions hosted in VS Code's Agents window:

- Typing `/rename` in an agent session's chat has no effect there — renaming is only available through the VS Code UI (verified 2026-07-23).
- There is no way for the **agent itself** to rename its session — no tool, and no slash-command it can run.

## Proposal

1. **Honor `/rename NEW_NAME` in VS Code agent sessions**, matching the terminal CLI behavior.
2. **Expose rename to the agent** (a tool, or agent-invocable `/rename`), so workflows can set titles programmatically.

## Use case

Session-hygiene rituals: I keep many long-running agent sessions and prefix titles with a status word as threads settle — `DONE …`, `PARKED …`, `CONT'D …` — so the session picker doubles as a work board. Today every close-out ends with manual rename homework; an agent-invocable rename would let the close-out workflow set the title itself (and lower-stakes: agents could title sessions descriptively from the start, cf. #3365 on auto-naming).

## Notes from poking at the internals

- A UI rename syncs into `~/.copilot/session-state/UUID/workspace.yaml` (`name:` + `user_named:`), so agents can already *read* current titles (verified 2026-07-24).
- Writing `workspace.yaml` directly doesn't work as a workaround: VS Code caches session labels elsewhere (workspace `state.vscdb`, `agentSessions.model.cache`) and doesn't notice the change.

## Related

- #1776 — added `/rename` (terminal CLI)
- #3365 — auto-generated session names not working
- #3415 — show session name at all times
- #2966 — broader session-management tooling

まず #1776 の既存のターミナル `/rename` 実装を追跡し、次にここで説明されている `workspace.yaml` と VS Code の `state.vscdb`/`agentSessions.model.cache` の動作を調べます。`/rename NEW_NAME` が VS Code のエージェントチャットで動作し、エージェントがセッション名を変更するためのサポートされた方法を持てば完了です。

索引モデルが issue の本文から書いたものです。