chore: upgrade example app to React Native 0.84.1

[mfazekas]

Upgrade the example app from React Native 0.82.0 to 0.84.1.

Updated dependencies

• react-native: 0.82.0 → 0.84.1
• react: 19.1.1 → 19.2.3
• react-dom: 19.1.0 → 19.2.3
• react-test-renderer: 19.1.1 → 19.2.3
• react-native-reanimated: 4.1.3 → 4.3.1
• react-native-worklets: 0.6.1 → 0.8.3
• @react-native/* devDeps: 0.82.0 → 0.84.1
• metro-config: 0.83.2 → 0.84.2

Also removes RCT-Folly and SocketRocket from the CI pod update command since these pods were removed in RN 0.84 (now bundled in prebuilt frameworks).

Test plan

• iOS build succeeds locally
• App launches and renders example list
• Unit tests pass (110/110)