feat(ui): explicit offline state inside an online game (+ offline word check)

When an online game loses the connection the game screen now says so and freezes
instead of silently greying out: a "connection lost" banner appears and the rack,
the move controls, the add-friend/block controls and the chat/dictionary entry all
disable (a started move stays a draft, committed by the player on reconnect). It is
driven off the net-state machine (netState.offline), so it also covers the
Telegram/VK mini-apps, where a lost connection was previously mute in-game.

If the player is already in the dictionary when the drop happens, the word check
falls back to the game's pinned on-device dictionary (exact when that dawg is
cached; "unavailable offline" otherwise) and the network-only complaint + external
look-up hide. Chat, when already open, keeps its existing read-only degrade
(send/nudge disable). New pure helper localWordCheck is unit-tested; the in-game
gating gets an e2e.

ui/e2e/ingame-ux.spec.ts

@@ -39,3 +39,38 @@ test('in-game UX: turn strip, bag badge + table footer, staged-play highlight an
   await expect(page.locator('.scorebadge')).toBeVisible();
   await expect(page.locator('.make')).toBeVisible();
 });
+
+test('online game offline: banner shows, the tray and comms entry freeze, and it thaws on recovery', async ({ page }) => {
+  await page.goto('/');
+  await page.getByRole('button', { name: /guest/i }).click();
+  await page.getByRole('button', { name: /🎲/ }).click();
+  await page.getByRole('button', { name: 'Random player' }).click();
+  await page.locator('.variant').first().click();
+  await page.getByRole('button', { name: /Start game/i }).click();
+  await page.evaluate(() => (window as unknown as { __mock: { joinOpponent(): void } }).__mock.joinOpponent());
+  await expect(page.getByText('Robo')).toBeVisible();
+
+  // Baseline online: no banner, the tray is interactive, the comms (chat/dictionary) entry is enabled.
+  await expect(page.locator('.offline-banner')).toHaveCount(0);
+  await expect(page.locator('.rack .tile').first()).toBeEnabled();
+
+  // The connection drops (the net hook rides past the hysteresis straight to offline).
+  await page.evaluate(() => (window as unknown as { __net: { offline(): void } }).__net.offline());
+
+  // The explicit "connection lost" banner appears and every rack tile freezes (cannot compose a move).
+  await expect(page.locator('.offline-banner')).toBeVisible({ timeout: 15000 });
+  const tiles = page.locator('.rack .tile');
+  const n = await tiles.count();
+  expect(n).toBeGreaterThan(0);
+  for (let i = 0; i < n; i++) await expect(tiles.nth(i)).toBeDisabled();
+
+  // The comms entry (💬 — chat + dictionary) is disabled; it lives in the history drawer, so open it.
+  await page.locator('.scoreboard').click();
+  await expect(page.locator('button:has(.chat-ico)')).toBeDisabled();
+
+  // Recovery: the network returns, the banner clears and the tray is interactive again.
+  await page.evaluate(() => (window as unknown as { __net: { online(): void } }).__net.online());
+  await expect(page.locator('.offline-banner')).toHaveCount(0, { timeout: 15000 });
+  await expect(page.locator('.rack .tile').first()).toBeEnabled();
+  await expect(page.locator('button:has(.chat-ico)')).toBeEnabled();
+});