feat: add PostHog analytics with full event tracking across app

Integrate self-hosted PostHog (SPM) with AnalyticsManager singleton wrapping
all SDK calls. Adds ~40 type-safe events covering trip planning, schedule,
progress, IAP, settings, polls, export, and share flows. Includes session
replay, autocapture, network telemetry, privacy opt-out toggle in Settings,
and super properties (app version, device, pro status, selected sports).

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -137,6 +137,46 @@ TripCreationView → TripCreationViewModel → PlanningRequest
 - CloudKit container ID: `iCloud.com.88oakapps.SportsTime`
 - `PDFGenerator` and `ExportService` are `@MainActor final class` (not actors) because they access MainActor-isolated UI properties and use UIKit drawing
 
+### Analytics (PostHog)
+
+All analytics go through `AnalyticsManager.shared` — never call PostHog SDK directly.
+
+**Architecture** (`Core/Analytics/`):
+- `AnalyticsManager.swift` - `@MainActor` singleton wrapping PostHogSDK. Handles init, tracking, opt-in/out, super properties, session replay.
+- `AnalyticsEvent.swift` - Type-safe enum with ~40 event cases, each with `name: String` and `properties: [String: Any]`.
+
+**Self-hosted backend:** `https://analytics.88oakapps.com`
+**API key:** Set in `AnalyticsManager.apiKey` (replace placeholder before shipping)
+
+**Features enabled:**
+- Event capture + autocapture
+- Session replay (`screenshotMode` for SwiftUI, text inputs masked)
+- Network telemetry capture
+- Super properties (app version, device model, OS, pro status, selected sports)
+- Privacy opt-out toggle in Settings (persisted via UserDefaults `"analyticsOptedOut"`)
+
+**Adding new analytics:**
+```swift
+// 1. Add case to AnalyticsEvent enum
+case myNewEvent(param: String)
+
+// 2. Add name and properties in the computed properties
+// 3. Call from anywhere:
+AnalyticsManager.shared.track(.myNewEvent(param: "value"))
+```
+
+**Correct Usage:**
+```swift
+// ✅ CORRECT - Use AnalyticsManager
+AnalyticsManager.shared.track(.tripSaved(tripId: id, stopCount: 3, gameCount: 5))
+AnalyticsManager.shared.trackScreen("TripDetail")
+
+// ❌ WRONG - Never call PostHog SDK directly
+PostHogSDK.shared.capture("trip_saved") // NO!
+```
+
+**Initialization:** Called during app bootstrap in `SportsTimeApp.performBootstrap()` (Step 7). Super properties refreshed on `.active` scene phase. Flushed on `.background`.
+
 ### Themed Background System
 
 All views use `.themedBackground()` modifier for consistent backgrounds app-wide.