docs: add multi-server chatbot quickstart example

[lil-goat]

Fixes #740

Summary

• Adds a multi-server chatbot example for examples/client-quickstart that connects to multiple stdio MCP servers and exposes their tools as one combined Anthropic tool list.
• Qualifies tool names with a stable server label, then routes tool calls back to the correct MCP client/server.
• Adds focused helper tests for server label sanitization, deduping, and qualified tool definitions.
• Documents how to run the multi-server variant from the client quickstart.

Validation

• corepack pnpm install --frozen-lockfile --ignore-scripts --offline --reporter append-only
• corepack pnpm --filter @modelcontextprotocol/examples-client-quickstart test
• corepack pnpm --filter @modelcontextprotocol/examples-client-quickstart typecheck
• corepack pnpm --filter @modelcontextprotocol/examples-client-quickstart build
• git diff --cached --check

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Latest commit: 87e96d6

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commit: 87e96d6