Add analytics integration for usage tracking

[StephanMeijer]

Context

Find processes document indexing and search requests across multiple services, but there is currently no analytics infrastructure to track usage patterns. Understanding how the API is used - which services index the most documents, search query patterns, peak usage times - would help with capacity planning and feature prioritization.

Requirements

• Implement event tracking for key operations:
  • index events: service name, document count (single vs bulk), language distribution
  • search events: service name, query characteristics (length, filters used), result count, response time
  • delete events: service name, document count
• Support integration with common analytics backends (e.g., PostHog, Amplitude, Segment, or a generic webhook)
• Make analytics configurable via environment variables (enable/disable, backend selection, endpoint URL)
• Ensure user privacy - do not track actual query content or document data, only aggregate metadata
• Events should be sent asynchronously to avoid impacting API latency (consider using the existing Celery infrastructure)

Technical notes

• The three main views to instrument are in core/views.py: IndexDocumentView, SearchDocumentView, DeleteDocumentsView
• Celery is already configured (CELERY_BROKER_URL in settings) and could be used for async event dispatch
• Consider a simple abstraction layer so different analytics backends can be swapped without code changes
• Existing logging already captures some of this data - analytics could complement rather than replace logging