feat(analytics): add consent-gated activation-funnel analytics via PostHog

Installs are up 615% but 7-day retention is ~0% and we had no analytics SDK
to see where users drop off. Adds a thin PostHog wrapper (src/lib/analytics.ts)
that tracks app_opened, connection_form_submitted, connection_attempted,
connection_succeeded/failed (with a coarse error_class, e.g. the known 401
auth bug), message_sent, and response_received.

PostHog was chosen over Aptabase for its GMS-free JS-only RN SDK (fine for
the F-Droid/no-Firebase build), EU-hosted/self-host option, and generous
free tier. Analytics shares the exact same consent flag as Sentry
(telemetry.ts now gates both) so zero network calls happen without explicit
opt-in.

Requires a new EXPO_PUBLIC_POSTHOG_KEY CI secret (wired into build.yml,
publish-fdroid.yml, publish-play-store.yml, and documented in
publish-app-store.yml alongside the existing Sentry secrets).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NJKAQ6HAikWGQK7PGZ5Y4E

package.json

@@ -14,6 +14,7 @@
   "dependencies": {
     "@expo/vector-icons": "^15.0.3",
     "@gorhom/bottom-sheet": "5.2.8",
+    "@react-native-async-storage/async-storage": "2.2.0",
     "@react-navigation/native": "^7.0.14",
     "@sentry/react-native": "~6.14.0",
     "@tanstack/react-query": "^5.62.0",
@@ -30,6 +31,7 @@
     "expo-secure-store": "~15.0.8",
     "expo-speech-recognition": "3.0.1",
     "expo-status-bar": "~3.0.9",
+    "posthog-react-native": "^4.57.0",
     "react": "19.1.0",
     "react-native": "0.81.5",
     "react-native-gesture-handler": "~2.28.0",
@@ -55,4 +57,4 @@
       ]
     }
   }
-}
+}