[DX] Auto-install / prompt-install `documentdb-agent-kit` skills alongside MCP

Goal

Bridge the gap between the API surface (MCP server) and the orchestration layer (skills).

What to ship

When the user runs npx documentdb-mcp init (or first-time start), detect their skills-aware client (Claude Code, Copilot CLI, etc.) and offer to install documentdb-agent-kit skills automatically:

We detected you're using Claude Code. Install DocumentDB skills for richer context? [Y/n]

If yes, run the equivalent of npx skills add microsoft/documentdb-agent-kit for the appropriate skills directory.

Acceptance criteria

• Opt-in, not forced.
• Detects at least: Claude Code, Copilot CLI, Cursor, VS Code (Copilot).
• Skips gracefully on clients that don't support skills.

Why

Most of the "developer experience" gap is actually solved by skills, not docs. Wiring them together removes a discovery step.

Depends on

• init wizard (Tier 2).

Start with the init wizard (Tier 2) and trace the first-time start path to find where client detection and prompts belong. Review how Claude Code, Copilot CLI, Cursor, and VS Code (Copilot) expose skills directories; done means opt-in installation works for supported clients and unsupported clients are skipped gracefully.