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>

SportsTime/Features/Home/Views/HomeView.swift

@@ -91,6 +91,13 @@ struct HomeView: View {
             .tag(4)
         }
         .tint(Theme.warmOrange)
+        .onChange(of: selectedTab) { oldTab, newTab in
+            let tabNames = ["Home", "Schedule", "My Trips", "Progress", "Settings"]
+            let newName = newTab < tabNames.count ? tabNames[newTab] : "Unknown"
+            let oldName = oldTab < tabNames.count ? tabNames[oldTab] : nil
+            AnalyticsManager.shared.track(.tabSwitched(tab: newName, previousTab: oldName))
+            AnalyticsManager.shared.trackScreen(newName)
+        }
         .sheet(isPresented: $showNewTrip) {
             TripWizardView()
                 .environment(\.isDemoMode, ProcessInfo.isDemoMode)
@@ -106,6 +113,9 @@ struct HomeView: View {
             }
         }
         .onAppear {
+            let tabNames = ["Home", "Schedule", "My Trips", "Progress", "Settings"]
+            let activeTabName = selectedTab < tabNames.count ? tabNames[selectedTab] : "Unknown"
+            AnalyticsManager.shared.trackScreen(activeTabName)
             if displayedTips.isEmpty {
                 displayedTips = PlanningTips.random(3)
             }
@@ -116,7 +126,7 @@ struct HomeView: View {
             }
         }
         .sheet(isPresented: $showProPaywall) {
-            PaywallView()
+            PaywallView(source: "home_progress_gate")
         }
     }
 
@@ -209,6 +219,10 @@ struct HomeView: View {
                                 HStack(spacing: Theme.Spacing.md) {
                                     ForEach(regionGroup.trips) { suggestedTrip in
                                         Button {
+                                            AnalyticsManager.shared.track(.suggestedTripTapped(
+                                                region: regionGroup.region.shortName,
+                                                stopCount: suggestedTrip.trip.stops.count
+                                            ))
                                             selectedSuggestedTrip = suggestedTrip
                                         } label: {
                                             SuggestedTripCard(suggestedTrip: suggestedTrip)