Stage 17 (#9): animated shuffle — tiles hop along a low parabola to new slots

Give each rack slot a stable id permuted with the letters on shuffle, so the keyed
rack reorders (rather than relabelling in place) and Svelte's animate directive fires.
hop flies each tile along a parabola (apogee ~half a tile height) with a duration that
scales with the horizontal distance (arc length): the longest 1<->7 swap takes ~0.5s,
shorter swaps land sooner. Ordinary reflow (place/recall) stays instant via a guard.
e2e locks that a shuffle preserves the rack's tile multiset.

ui/e2e/game.spec.ts

@@ -48,6 +48,19 @@ test('a pending tile recalls on double-tap, not on a single tap', async ({ page
   await expect(page.locator('[data-cell].pending')).toHaveCount(0);
 });
 
+test('shuffle reorders the rack but keeps the same tiles', async ({ page }) => {
+  await openGame(page);
+  const before = await page.locator('.rack .tile').allTextContents();
+  expect(before.length).toBeGreaterThan(1);
+
+  await page.locator('button:has-text("🔀")').click(); // the shuffle tab (no pending tiles)
+  await page.waitForTimeout(650); // let the hop animation settle
+
+  // Same multiset of tiles after the shuffle — no tile is dropped or duplicated.
+  const after = await page.locator('.rack .tile').allTextContents();
+  expect([...after].sort()).toEqual([...before].sort());
+});
+
 test('history slides the board down and closes on a board tap', async ({ page }) => {
   await openGame(page);
   await page.locator('.burger').click();