feat(ui): single-word rule indicators + auto-match select redesign

Surface the per-game "single word" rule to the client and refine the
random-opponent New Game screen.

- Wire: thread multiple_words_per_turn into the GameView and Invitation
  FlatBuffers tables (Go + TS regenerated), through pkg/wire builders and both
  the backend push-event and gateway REST paths.
- In-game indicators (single-word games only): a small 1 in the status bar's
  score-preview slot (yields to the live preview) and a centred "One word per
  turn" label in the history-drawer header. Standard games show neither.
- Invitation card gains a "One word per turn" line for single-word invitations.
- Auto-match redesign: variant plaques are mutually-exclusive selects (highlight
  on tap, no longer enqueue); a lone offered variant is pre-selected; a bottom
  "Start game" button (disabled until a variant is chosen) confirms. The rule
  toggle appears once a Russian variant is selected.
- Tests: e2e for the new auto flow and the in-game indicator (mock g3 is a
  single-word game); mock/data + fixtures carry the new field. Docs: UI_DESIGN.

ui/e2e/game.spec.ts

@@ -70,16 +70,35 @@ test('new game: variant buttons show a rules summary and the move-limit', async
   await expect(page.locator('.movelimit')).toBeVisible(); // turn-time under the buttons
 });
 
-test('new game: Russian games offer the "multiple words per turn" toggle, off by default', async ({ page }) => {
+test('new game: auto-match selects a variant, then a Russian pick reveals the off-by-default toggle', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
   await page.getByRole('button', { name: /New/ }).click(); // auto-match
-  // The mock session supports Russian, so the single-word-rule toggle is offered and starts off.
+  // Several variants are offered, so nothing is selected: Start is disabled and there is no toggle yet.
+  const start = page.getByRole('button', { name: /Start game/i });
+  await expect(start).toBeDisabled();
+  await expect(page.getByLabel('Multiple words per turn')).toHaveCount(0);
+  // Selecting the Russian Scrabble variant highlights it, enables Start, and reveals the rule toggle (off).
+  await page.locator('.variant', { hasText: 'Скрэббл' }).click();
+  await expect(page.locator('.variant.selected')).toHaveCount(1);
+  await expect(start).toBeEnabled();
   const toggle = page.getByLabel('Multiple words per turn');
   await expect(toggle).toBeVisible();
   await expect(toggle).not.toBeChecked();
-  await toggle.check();
-  await expect(toggle).toBeChecked();
+});
+
+test('single-word game shows the one-word indicator in the status bar and the history header', async ({ page }) => {
+  await page.goto('/');
+  await page.getByRole('button', { name: /guest/i }).click();
+  // g3 is a finished Russian single-word game (vs Rick); open it from the lobby.
+  await page.getByRole('button', { name: /Rick/ }).click();
+  await expect(page.locator('[data-cell]').first()).toBeVisible();
+  await expect(page.locator('.pane')).toHaveCount(1);
+  // The status bar carries the small "1️⃣" indicator (single-word, nothing pending).
+  await expect(page.locator('.oneword')).toBeVisible();
+  // Tapping the scoreboard opens the history, whose header shows the spelled-out rule label.
+  await page.locator('.scoreboard').click();
+  await expect(page.locator('.oneword-label')).toBeVisible();
 });
 
 test('a pending tile recalls on double-tap, not on a single tap', async ({ page }) => {