Update example app for modern Expo Go versions

[ZainKazmiii]

Fixes #339

Summary

• update the example app from legacy Expo SDK 36-era dependencies to Expo SDK 43-era dependencies
• migrate the example tab navigator to @react-navigation/* APIs used by current Expo Go stacks
• replace class-based font-loading bootstrap with useFonts + expo-app-loading
• remove pinned sdkVersion from example/app.json so the example aligns with modern Expo configuration
• refresh example local run instructions to npm commands
• add example/tsconfig.json aligned with Expo TypeScript defaults

Validation

I attempted to run npm install --no-audit --no-fund in example/ with retry/fallback commands, but this runner could not complete dependency installation due environment/network restrictions (ECONNREFUSED 127.0.0.1:9, plus earlier npm cache permission issues).

[ZainKazmiii]

Quick follow-up on this bounty PR.

I rechecked the current PR head and there are no failed or pending checks on my side. If you want any updates (example app wording, Expo config, or compatibility notes), I can adjust quickly.