chore(mobile): upgrade to Expo SDK 56

Bump expo, react, react-native, and all expo-* / react-native-* peers to
the SDK 56 line via expo install --fix, adding expo-splash-screen and
expo-system-ui for config plugins the SDK split out of core. Bump
@bacons/apple-targets, react-native-view-shot, and other native modules
to versions compatible with React Native 0.85 and the new architecture.

Remove @react-navigation/* direct dependencies and route their hooks
through expo-router, which is no longer compatible with react-navigation
as of SDK 56. Fix RN 0.85's removed StyleSheet.absoluteFillObject (use
absoluteFill) and react-native-view-shot 5.x's ViewShotRef type across
call sites. Downgrade eslint-plugin-react-hooks v7's new React Compiler
era rules to warnings pending a dedicated refactor, and repair Jest
fallout from the jest-expo/reanimated/worklets/expo-media-library bumps.

Regenerate the committed ios/ and android/ native projects with
`expo prebuild --clean` (required for @bacons/apple-targets 5.x) against
the production release channel, and document that requirement.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/mobile/android/app/src/main/res/values/styles.xml

@@ -1,18 +1,14 @@
 <resources xmlns:tools="http://schemas.android.com/tools">
-  <style name="AppTheme" parent="Theme.AppCompat.Light.NoActionBar">
-    <item name="android:enforceNavigationBarContrast" tools:targetApi="29">true</item>
-    <item name="android:textColor">@android:color/black</item>
-    <item name="android:editTextStyle">@style/ResetEditText</item>
+  <style name="AppTheme" parent="Theme.AppCompat.DayNight.NoActionBar">
     <item name="android:editTextBackground">@drawable/rn_edit_text_material</item>
     <item name="colorPrimary">@color/colorPrimary</item>
-    <item name="android:statusBarColor">#1a1a2e</item>
+    <item name="android:statusBarColor">@android:color/transparent</item>
+    <item name="android:navigationBarColor">@android:color/transparent</item>
   </style>
-  <style name="ResetEditText" parent="@android:style/Widget.EditText">
-    <item name="android:padding">0dp</item>
-    <item name="android:textColorHint">#c8c8c8</item>
-    <item name="android:textColor">@android:color/black</item>
-  </style>
-  <style name="Theme.App.SplashScreen" parent="AppTheme">
-    <item name="android:windowBackground">@drawable/ic_launcher_background</item>
+  <style name="Theme.App.SplashScreen" parent="Theme.SplashScreen">
+    <item name="windowSplashScreenBackground">@color/splashscreen_background</item>
+    <item name="windowSplashScreenAnimatedIcon">@drawable/splashscreen_logo</item>
+    <item name="postSplashScreenTheme">@style/AppTheme</item>
+    <item name="android:windowSplashScreenBehavior">icon_preferred</item>
   </style>
 </resources>