Fix backend test suite failures

### Overview
The backend test suite has several pre-existing failures that predate the ESM migration. These need to be resolved so the test suite can serve as a reliable quality gate.

### Action Items
- [ ] Router tests (`auth`, `events`, `projects`, `users`) fail because `process.env.CUSTOM_REQUEST_HEADER` is undefined — tests should set required env vars themselves
- [ ] `models/event.model.test.js` and `models/projectTeamMember.model.test.js` have `updatedDate` assertions that fail because Mongoose pre-update hooks aren't firing on `findOneAndUpdate` and `updateMany`
- [ ] `setup-test.js` has un-awaited `deleteMany()` calls causing race conditions between tests
- [ ] MongoMemoryServer teardown produces `MongoNetworkError: connection closed` errors from parallel test execution
- [ ] Empty `describe` blocks cause Vitest to fail (Jest silently skipped them)

### Resources/Instructions
- Related: #2133 (ESM migration)
- Backend test runner: Vitest (migrated from Jest as part of #2133)