feat(analytics): add core analytics infrastructure with PostHog integration

- Implement comprehensive analytics type system with 100+ event types
- Create event builders for consistent event tracking
- Add main analytics service with PostHog integration
- Include performance tracking utilities with percentile monitoring
- Support anonymous user tracking with session management
- Implement sanitization helpers to remove PII from events
- Add event queueing with automatic flush intervals
- Support for screen tracking and app context

BREAKING CHANGE: Analytics tracking is now integrated throughout the app
and requires PostHog API key configuration via environment variables.