Migrate backend from CommonJS to ES Modules

[trillium]

Overview

The backend uses CommonJS (require/module.exports) while shared/ already uses ESM, causing test failures. The backend should be fully migrated to ES Modules for consistency and to unblock the shared module imports.

Action Items

• Convert all third-party require() to import statements (36 files)
• Convert all relative require() to import with .js extensions (41 files)
• Convert all module.exports to export default/named exports (47 files)
• Replace require.main === module with import.meta.url pattern (5 files)
• Replace __dirname with fileURLToPath(import.meta.url) (1 file)
• Add "type": "module" to backend/package.json
• Migrate test runner from Jest to Vitest (client already uses Vitest)
• Convert all jest.mock/jest.fn/jest.spyOn to Vitest equivalents

Resources/Instructions

• Node.js ESM docs: https://nodejs.org/api/esm.html
• Vitest migration from Jest: https://vitest.dev/guide/migration.html
• Draft branch: chore/backend-esm-migration