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

Bắt đầu bằng cách lần theo triển khai `/rename` hiện có trên terminal từ #1776, sau đó kiểm tra `workspace.yaml` và hành vi của `state.vscdb`/`agentSessions.model.cache` trong VS Code được mô tả ở đây. Hoàn thành khi `/rename NEW_NAME` hoạt động trong chat agent của VS Code và một agent có cách được hỗ trợ để đổi tên session của mình.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.