feat: add user accounts, authentication, and game history with Prisma 7

- Implement user registration and login with NextAuth v5 (email/password, JWT)
- Add authentication modal in UI with login/register tabs
- Create user profile screen showing game statistics and history
- Integrate Prisma 7 ORM with SQLite database for data persistence
- Store game results (mode, path, clicks, time) in database
- Auto-save completed games only when user is authenticated
- Separate business logic into reusable hooks (useSoloGame, useMultiGame)
- Organize UI into composable screen components (HomeScreen, SoloScreen, ProfileScreen, etc)
- Add session persistence across F5 refresh for solo and multiplayer
- Style auth modal, account button, and profile stats dashboard

lib/types.ts

@@ -0,0 +1,11 @@
+export type Screen = "home" | "lobby" | "game" | "solo" | "profile";
+
+export type WikiArticle = {
+  title: string;
+  html: string;
+};
+
+export type Puzzle = {
+  start: string;
+  target: string;
+};