Refactor Dockerfile, entrypoint script, and README for streamlined uv integration

- Added `UV_NO_CACHE` environment variable to Dockerfile for improved dependency handling.
- Updated entrypoint commands to use `uv run` for Python scripts and migrations.
- Enhanced README with detailed `uv` usage instructions, including installation, dependency management, and troubleshooting.
- Removed outdated `PATH` modifications for `uv` binaries in Dockerfile.

backend/entrypoint.sh

@@ -3,10 +3,10 @@ set -e
 echo "Starting Backend"
 
 # Apply database migrations
-alembic upgrade head
+uv run alembic upgrade head
 
 # Initialize database (creates first superuser if needed)
-python app/init_db.py
+uv run python app/init_db.py
 
 # Execute the command passed to docker run
 exec "$@"