refactor: extract reusable library

- move reusable domain, data, state, ui code into src/lib
- update host screens to consume new library exports
- document architecture and configure path aliases
- bump astro integration dependencies for compatibility

Refs #30

src/lib/index.ts

@@ -0,0 +1,9 @@
+export * from './domain';
+export * from './data';
+export * from './state';
+export * from './ui';
+export * from './features/game-list';
+export * from './features/game-detail';
+export * from './features/game-lifecycle';
+export * from './features/new-game';
+