Build a Task Management API

Problem/Feature Description

Build a REST API for a small team productivity tool using Express and TypeScript.

Data model:

• Task: { id, title, description, status, assigneeEmail, createdAt }
• Status must be one of: "todo", "in_progress", "done"

Endpoints:

• GET /api/tasks -- list all tasks, optionally filter by ?status=todo query param
• GET /api/tasks/:id -- get a single task
• POST /api/tasks -- create a task (title required, status defaults to "todo")
• PATCH /api/tasks/:id -- update task fields (validate status enum if provided)
• DELETE /api/tasks/:id -- delete a task

Business rules:

• Title must be a non-empty string, max 200 characters
• If assigneeEmail is provided, it must contain an @ symbol
• Cannot transition status from "done" back to "todo" (only "done" -> "in_progress" is allowed as a backward step)

Use in-memory storage. Include package.json with dependencies.

Output Specification

Produce:

• src/server.ts -- server entry point
• src/app.ts -- Express application setup
• src/routes/tasks.ts -- route handlers
• package.json -- with dependencies listed

You may create additional files for a well-organized codebase.