fix: use subprocess for alembic migrations to avoid async/sync issues

SQLAlchemy 2.0 async engines conflict with alembic's sync context manager.
Instead of trying to bridge async/sync, use subprocess to run
'alembic upgrade head' directly. This is simpler and more reliable.

- Remove psycopg2-binary dependency (no longer needed)
- Simplify init_database to use subprocess.run()
- Remove all sync engine code

apps/api/pyproject.toml

@@ -8,7 +8,6 @@ dependencies = [
     "uvicorn[standard]>=0.24.0",
     "sqlalchemy>=2.0.0",
     "asyncpg>=0.29.0",
-    "psycopg2-binary>=2.9.0",
     "alembic>=1.12.0",
     "pydantic>=2.5.0",
     "pydantic-settings>=2.1.0",