feat(examples): Add LSP TypeScript example project

[amondnet]

Summary

Add a TypeScript example project to demonstrate LSP functionality testing.

Description

Create an example project at examples/lsp-typescript/ that showcases:

• LSPManager API usage (diagnostics, hover, definition, references, completion)
• TypeScript language server integration
• Interactive demo script for testing LSP features

Tasks

• T001 [P] Create example directory structure (examples/lsp-typescript/)
• T002 [P] Create package.json with dependencies
• T003 [P] Create tsconfig.json for TypeScript configuration
• T004 Create demo.ts LSP demonstration script
• T005 Create src/index.ts entry point
• T006 Create src/utils/math.ts utility module (with intentional type errors for testing)
• T007 Create README.md with usage documentation

Files to Create

examples/lsp-typescript/
├── README.md
├── package.json
├── tsconfig.json
├── demo.ts
└── src/
    ├── index.ts
    └── utils/
        └── math.ts

Acceptance Criteria

• Example can be run with bun run demo.ts
• Demonstrates diagnostics detection for type errors
• Shows hover, definition, and completion functionality
• README documents all features and usage

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• To see the specific tasks where the Asana app for GitHub is being used, see below:
  • https://app.asana.com/0/0/1212822778943945