Archive legacy Flask implementation

[AlexKitipov]

Motivation

• Remove confusion caused by a leftover Flask/SQLite example that could be mistaken for the active backend.
• Ensure the repository documents and deploys a single application architecture (FastAPI + PostgreSQL + React).

Description

• Moved the legacy app.py and schema.sql from the repository root into examples/legacy-flask/ to preserve them as an archived example while removing them from the active root.
• Updated README.md to document the active stack (app.main:app FastAPI backend, SQLAlchemy + Alembic migrations, PostgreSQL, and the React/TypeScript frontend) and adjusted the project structure and run instructions accordingly.
• Verified deployment and Docker/service configuration targets the FastAPI application and left production/dev deployment files unchanged.
• Committed the archive and README changes under the message "Archive legacy Flask implementation".

Testing

• Ran the test suite with pytest -q, which completed successfully (all tests passed).

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Codex Task