fix(ads): fire the hint interstitial on the confirmed move, not on the hint

Taking a hint fired the post-move interstitial immediately, when the hint's
preview tiles landed — interrupting the turn and reverting the board to the
rack on the ad's close while the hint stayed spent. Move the trigger to the
move confirmation: a hint applied this turn marks it (hintUsedThisTurn), and
the confirmed play fires the hint-kind interstitial (its own cooldown)
instead of the plain move one; the marker clears on any turn boundary
(applyMoveResult) so a hint-then-pass does not leak into the next move.

e2e: taking a hint fires no ad; confirming a move does.

ui/e2e/game.spec.ts

@@ -48,6 +48,33 @@ test('placing a tile and confirming via ✅ commits the move', async ({ page })
   await expect(page.locator('.make')).toBeHidden();
 });
 
+// Regression: taking a hint must NOT fire the post-move interstitial. Firing on the hint interrupted
+// placing the preview and reverted the board on the ad's close while the hint stayed spent (the
+// reported bug). In mock mode the ad stub shows an "ad fired" toast, standing in for a real VK ad.
+test('taking a hint does not fire the interstitial', async ({ page }) => {
+  await openGame(page);
+  // Take a hint (the control confirms on a second tap). It produces a legal preview, so the ✅
+  // control appears — proof the hint fired.
+  const hint = page.getByRole('button', { name: 'Hint' });
+  await hint.click();
+  await hint.click();
+  await expect(page.locator('.make')).toBeVisible();
+  // A spurious ad would have toasted by now; none may.
+  await page.waitForTimeout(400);
+  await expect(page.getByText('ad fired')).toHaveCount(0);
+});
+
+// The interstitial fires once the move is CONFIRMED (never on the hint / pass / exchange / resign).
+test('confirming a move fires the interstitial', async ({ page }) => {
+  await openGame(page);
+  await page.locator('.rack .tile').first().click();
+  await page.locator('[data-cell]:not(.filled)').nth(30).click();
+  await expect(page.locator('[data-cell].pending')).toHaveCount(1);
+
+  await page.locator('.make').click();
+  await expect(page.getByText('ad fired')).toBeVisible();
+});
+
 test('a placed tile is saved as a draft and restored on reopening the game', async ({ page }) => {
   await openGame(page);
   await page.locator('.rack .tile').first().click();