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/features/new-game/index.ts

@@ -0,0 +1,9 @@
+export { PlayerSelectModal } from './steps/PlayerSelectModal';
+export { Player1Step } from './steps/Player1Step';
+export { Player2Step } from './steps/Player2Step';
+export { Player3Step } from './steps/Player3Step';
+export { GameTypeStep } from './steps/GameTypeStep';
+export { RaceToStep } from './steps/RaceToStep';
+export { BreakRuleStep } from './steps/BreakRuleStep';
+export { BreakOrderStep } from './steps/BreakOrderStep';
+