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/useTimer.ts

@@ -0,0 +1,45 @@
+import { useState, useEffect, useCallback, useRef } from "react";
+
+export function useTimer() {
+  const [elapsed, setElapsed] = useState(0);
+  const startTimeRef = useRef<number | null>(null);
+  const rafRef = useRef<number | null>(null);
+
+  const startRef = useRef(() => {
+    startTimeRef.current = performance.now();
+    function tick() {
+      if (startTimeRef.current !== null) {
+        setElapsed((performance.now() - startTimeRef.current) / 1000);
+        rafRef.current = requestAnimationFrame(tick);
+      }
+    }
+    rafRef.current = requestAnimationFrame(tick);
+  });
+
+  const stopRef = useRef((): number => {
+    let final = 0;
+    if (startTimeRef.current !== null) {
+      final = (performance.now() - startTimeRef.current) / 1000;
+      setElapsed(final);
+    }
+    if (rafRef.current !== null) {
+      cancelAnimationFrame(rafRef.current);
+      rafRef.current = null;
+    }
+    startTimeRef.current = null;
+    return final;
+  });
+
+  const resetRef = useRef(() => {
+    stopRef.current();
+    setElapsed(0);
+  });
+
+  const start = useCallback(() => startRef.current(), []);
+  const stop = useCallback(() => stopRef.current(), []);
+  const reset = useCallback(() => resetRef.current(), []);
+
+  useEffect(() => () => { if (rafRef.current !== null) cancelAnimationFrame(rafRef.current); }, []);
+
+  return { elapsed, start, stop, reset };
+}