Add expo-system-ui so userInterfaceStyle actually applies on Android

[toruiwasa]

Raised by the review of PR #110 (Task 9 / #12).

Field	Contents
Goal	The userInterfaceStyle: "light" pin in app.json takes effect on Android, not only on iOS.
Context	PR #110 pinned userInterfaceStyle to "light" because colors.ts ships a light palette only, so "automatic" would pair dark system chrome with light screens. That reasoning holds — but Expo's app config reference states, for both userInterfaceStyle and android.userInterfaceStyle: "Requires expo-system-ui be installed in your project to work on Android." expo-system-ui is not in apps/mobile/package.json and is not a transitive dependency of expo, so on Android the pin is inert and the recorded rationale claims an invariant only iOS gets. PR #110 corrected the comment in colors.ts to say so rather than adding a native module it could not verify.
Scope	Add expo-system-ui to apps/mobile and confirm the pin applies on an Android device in system dark mode. Open decision: whether to add the package or instead drop the pin and commit to supporting dark mode on both platforms — if #111 lands a dark palette first, this issue is moot and should be closed as such.
Test boundary	Nothing unit-testable — the property is consumed by the native build, not by JS. Verification is manual on a device: Android in system dark mode shows light chrome.
Done when	An Android development build in system dark mode renders light system chrome, matching the palette, and the caveat paragraph in colors.ts is removed.
Branch	fix/mobile-android-ui-style
Dependency	#95 — adding a native module needs an EAS development build to verify, and #95 is what makes cloud builds possible.
Risk	LOW — no screen reads useColorScheme today, so nothing is currently mis-rendering; the change adds a native module, which is why it needs a device build rather than CI.