Task Management REST API

Problem/Feature Description

A small team wants a task management backend built with Flask. They need a REST API where users can create projects and add tasks to them. Each task has a title, description, status (todo/in_progress/done), and priority (low/medium/high). Each project has a name and description.

The team specifically wants:

1. A clean, well-structured Flask project they can extend later with authentication and real database support.
2. Proper error handling -- if a project or task doesn't exist, the API should return a clear JSON error. Validation errors (missing title, invalid status) should also return structured JSON.
3. CORS enabled so their React frontend can call the API.
4. For now, an in-memory data store is fine (dictionaries/lists), but the structure should make it easy to swap in a real database later.

Build the complete Flask application with endpoints for:

• POST /api/projects -- create a project
• GET /api/projects -- list all projects
• GET /api/projects/<id> -- get a single project
• POST /api/projects/<id>/tasks -- create a task in a project
• GET /api/projects/<id>/tasks -- list tasks in a project
• PATCH /api/tasks/<id> -- update a task's status or priority

Output Specification

Produce Python source files in a task-manager/ directory:

• app/__init__.py -- application factory
• app/extensions.py -- extension instances
• app/errors.py -- custom exceptions and error handler registration
• app/routes/projects.py -- project blueprint
• app/routes/tasks.py -- task blueprint
• app/db.py -- in-memory data store
• tests/conftest.py -- test fixtures
• run.py -- entry point
• requirements.txt

Do not run pip install or start the server.