Add example: Real-world web server debugging

[ibrahimcesar]

Create a comprehensive example showing async-inspect with a real web server.

Description

Create an example that demonstrates debugging common async web server issues:

• Slow database queries
• Lock contention
• Connection pool exhaustion
• Request timeouts

Goals

• Realistic axum or actix-web application
• Demonstrates multiple async-inspect features
• Well-commented for learning

Suggested Structure

examples/web_server_debugging/
├── main.rs           # Web server with intentional issues
├── handlers.rs       # Request handlers
├── database.rs       # Simulated slow queries
└── README.md         # How to run and debug

Features to Demonstrate

• Task tracking for requests
• Lock contention detection
• Slow query identification
• TUI monitoring

Acceptance Criteria

• Working example with README
• At least 3 debuggable scenarios
• Comments explaining what to look for
• Works with cargo run --example