[mega-issue] Spring (summer) cleaning

[MangoSwirl]

There's no new game to implement, so now is a great time to work on some internal changes to improve on our code's readability and minimize friction in the development process. Here's the current plan.

• Switch over queries to use React Query
• Use Zod for API response validation rather than trustfully casting
• Use URLSearchParams for GET parameters
• Set up ESLint, Prettier, and enforce in CI
• Set up OTA updates via expo-updates
• Set up deployment workflows with EAS Submit