Transition back-end tests to vitest

[ahdriel]

Features and Changes

• Migrated all 39 test files within packages/back-end from Jest to Vitest.
• Replaced all Jest-specific syntax (e.g., jest.mock, jest.fn, jest.spyOn, jest.useFakeTimers) with their Vitest equivalents (vi.mock, vi.fn, vi.spyOn, vi.useFakeTimers).
• Introduced vitest.config.ts for backend test configuration.
• Updated packages/back-end/package.json to include Vitest scripts and dependencies.
• Added packages/back-end/VITEST-MIGRATION-COMPLETE.md to document the completed migration and key patterns.

Dependencies

None

Testing

• Navigate to the packages/back-end directory.
• Run yarn test to execute all migrated tests using Vitest.
• Verify all tests pass.

Screenshots

N/A