Convert backend workers to TypeScript

### Overview
Convert the backend worker modules (openCheckins, closeCheckins, createRecurringEvents, slackbot, tokenCleanup) to TypeScript to catch type errors at compile time — particularly around date/time handling which has been a source of bugs (#1872).

### Action Items
- [ ] Add TypeScript and required @types packages to backend
- [ ] Create tsconfig.json for backend
- [ ] Define types for Event, CheckIn, RecurringEvent models
- [ ] Convert worker files from .js to .ts
- [ ] Update build/dev scripts to handle TypeScript compilation
- [ ] Ensure compatibility with ESM migration (#2133)

### Resources/Instructions
- Depends on: #2133 (ESM migration) should be merged first
- Related: #1872 (timezone bug in workers)