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/Paywall/ViewModifiers/ProGate.swift

@@ -30,7 +30,7 @@ struct ProGateModifier: ViewModifier {
                 }
             }
             .sheet(isPresented: $showPaywall) {
-                PaywallView()
+                PaywallView(source: "pro_gate_\(feature.rawValue)")
             }
     }
 }
@@ -53,7 +53,7 @@ struct ProGateButtonModifier: ViewModifier {
             content
         }
         .sheet(isPresented: $showPaywall) {
-            PaywallView()
+            PaywallView(source: "pro_gate_\(feature.rawValue)")
         }
     }
 }