[FEATURE] VS Code integration: support contributes.chatSkills for parity with GitHub Copilot

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

VS Code has an official "Agent Skills" extension contribution point — contributes.chatSkills in package.json (https://code.visualstudio.com/docs/agent-customization/agent-skills#_contribute-skills-from-extensions). Any VS Code extension can bundle a SKILL.md and have it surfaced automatically; per that page, GitHub Copilot (in VS Code, its CLI, and its cloud agent) consumes this with zero user action.

Claude Code's VS Code integration doesn't appear to read this contribution point — skill discovery is filesystem-only (.claude/skills/*/SKILL.md in the workspace, or ~/.claude/skills/). That means an extension author who wants to support both Copilot and Claude Code has to build a bespoke mechanism (e.g. an "install skills into .claude/skills/" command) to reach Claude Code, duplicating exactly what chatSkills was designed to make automatic.

Concrete motivating case: building a VS Code extension (bundling three SKILL.md files under contributes.chatSkills) and hitting exactly this gap.

### Proposed Solution

So, the feature request is for the Claude Code VS Code integration to also read contributes.chatSkills from active extensions, the same way Copilot does, so adopting the standard contribution point covers both agents without extra per-extension plumbing.

### Alternative Solutions

The alternative is that the user of an extension must locate the skills and manually copy it into the workspace.

### Priority

Medium - Would be very helpful

### Feature Category

Configuration and settings

### Use Case Example

_No response_

### Additional Context

_No response_

Start by locating the VS Code integration and its existing skill-discovery path, then review the contributes.chatSkills contribution point in package.json and the linked VS Code documentation. Done means skills bundled by active extensions are discovered without manual copying, while the existing .claude/skills and ~/.claude/skills sources continue to work.

Written by the indexing model from the issue text.