Add an agent-maintained skill to keep repo docs up to date

## Motivation

Agents (Copilot, MCP-based assistants, etc.) increasingly perform tasks in this repo by reading the docs and instructions we ship (`AGENTS.md`, `.github/copilot-instructions.md`, `.github/skills/`, `doc/dev/`, etc.). The quality of those docs directly affects the agent''s success rate: if the docs are stale, incomplete, or inconsistent with the current code/tooling, the agent gets the wrong info and produces worse results.

If we can **refresh and check the docs in time**, an agent can pull the right information straight from the repo and complete tasks more reliably.

## Proposal

Create a **skill (or reusable pattern)** that leverages an agent to keep this repo''s docs up to date. This skill will be **written and maintained by the agent itself** — the agent decides the checklist, method, and solutions for keeping docs accurate and self-consistent.

## Goal

Improve agent task success rate by ensuring repo docs are accurate, current, and self-consistent — so agents get the right info directly from the repo.