fix(mobile): align expo-* package versions with SDK 52

Phase 0 installed expo-application/expo-image-picker/expo-dev-client at
^55.x assuming the major version matched the SDK number. It doesn't —
each expo-* package has its own major. Misaligned versions pulled in
expo-modules-core@2.2.3 which expects an API that SDK 52's gradle plugin
host doesn't provide, breaking the Gradle build with
'expo-module-gradle-plugin not found'.

`expo install --fix` aligned everything to SDK 52 baselines:
  expo-application 55.0.15 -> ~6.0.2
  expo-dev-client  55.0.33 -> ~5.0.20
  expo-image-picker 55.0.20 -> ~16.0.6
  expo-sqlite      15.0.6  -> ~15.1.4
  react-native     0.76.0  -> 0.76.9
  + RN companion libs (gesture-handler, screens, async-storage)

apps/mobile/package.json

@@ -23,26 +23,26 @@
     "@config-plugins/react-native-webrtc": "^10.0.0",
     "@livekit/react-native": "^2.10.3",
     "@livekit/react-native-webrtc": "^144.0.0",
-    "@react-native-async-storage/async-storage": "^3.0.2",
+    "@react-native-async-storage/async-storage": "^1.23.1",
     "@supabase/supabase-js": "^2.46.0",
     "expo": "^52.0.0",
-    "expo-application": "^55.0.15",
+    "expo-application": "^6.0.2",
     "expo-constants": "~17.0.0",
-    "expo-dev-client": "^55.0.33",
+    "expo-dev-client": "^5.0.20",
-    "expo-image-picker": "^55.0.20",
+    "expo-image-picker": "^16.0.6",
     "expo-linking": "~7.0.0",
     "expo-notifications": "~0.29.0",
     "expo-router": "~4.0.0",
     "expo-secure-store": "~14.0.0",
-    "expo-sqlite": "~15.0.0",
+    "expo-sqlite": "~15.1.4",
     "expo-status-bar": "~2.0.0",
     "livekit-client": "^2.7.0",
     "react": "18.3.1",
-    "react-native": "0.76.0",
+    "react-native": "0.76.9",
-    "react-native-gesture-handler": "^2.31.2",
+    "react-native-gesture-handler": "^2.20.2",
     "react-native-libsodium": "^1.3.0",
     "react-native-safe-area-context": "~4.12.0",
-    "react-native-screens": "~4.1.0"
+    "react-native-screens": "~4.4.0"
   },
   "devDependencies": {
     "@babel/core": "^7.25.0",