feat(backend): integrate PostHog analytics for enhanced observability

- Added PostHog configuration options to .env.example files for both Docker and Surfsense backend.
- Introduced PostHog dependency in pyproject.toml.
- Implemented analytics middleware to capture various events across the application, including user authentication, automation runs, and API requests.
- Enhanced existing routes and services to emit analytics events, providing insights into user interactions and system performance.
- Ensured graceful shutdown of analytics clients in worker processes and application lifecycles.

surfsense_backend/.env.example

@@ -555,6 +555,14 @@ LANGSMITH_PROJECT=surfsense
 # OTEL_METRIC_EXPORT_INTERVAL=300000                       # ms; 5 minutes
 # OTEL_SDK_DISABLED=true                                  # emergency kill-switch
 
+# Observability - PostHog product analytics (server-side)
+# Opt-in like OTel: leave POSTHOG_API_KEY unset for zero telemetry. Use the
+# SAME project key as the frontend's NEXT_PUBLIC_POSTHOG_KEY so server events
+# merge onto the persons the web app already identifies by user id.
+# POSTHOG_API_KEY=phc_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
+# POSTHOG_HOST=https://us.i.posthog.com
+# POSTHOG_AI_PRIVACY_MODE=true   # false ships LLM prompt/completion bodies to PostHog
+
 # Skills + subagents
 # SURFSENSE_ENABLE_SKILLS=false
 # SURFSENSE_ENABLE_SPECIALIZED_SUBAGENTS=false