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/src/screens/NewGame.svelte

@@ -24,7 +24,12 @@
   // "Multiple words per turn" off is the single-word rule; it is offered for Russian games
   // only (English is always standard and shows no toggle). Shared by both flows.
   let multipleWords = $state(false);
-  const autoHasRussian = $derived(variants.some((v) => supportsMultipleWordsToggle(v.id)));
+  // Auto-match: the variant is a select (highlight, no immediate enqueue) confirmed by the
+  // Start button. A lone offered variant is pre-selected; with several the player must pick.
+  let selectedAuto = $state<Variant | ''>('');
+  $effect(() => {
+    if (variants.length === 1 && !selectedAuto) selectedAuto = variants[0].id;
+  });
   const timeouts = [
     { secs: 300, key: 'time.minutes' as MessageKey, n: 5 },
     { secs: 1800, key: 'time.minutes' as MessageKey, n: 30 },
@@ -182,15 +187,14 @@
 
       {#if mode === 'auto'}
         <p class="subtitle">{t('new.subtitle')}</p>
-        {#if autoHasRussian}
-          <label class="toggle">
-            <span>{t('new.multipleWordsPerTurn')}</span>
-            <input type="checkbox" bind:checked={multipleWords} />
-          </label>
-        {/if}
         <div class="variants">
           {#each variants as v (v.id)}
-            <button class="variant" onclick={() => find(v.id)} disabled={!connection.online}>
+            <button
+              class="variant"
+              class:selected={selectedAuto === v.id}
+              onclick={() => (selectedAuto = v.id)}
+              disabled={!connection.online}
+            >
               <span class="vmain">
                 <span class="vname">{t(v.label)}</span>
                 {#if VARIANT_FLAG[v.id]}
@@ -203,7 +207,18 @@
             </button>
           {/each}
         </div>
+        {#if selectedAuto && supportsMultipleWordsToggle(selectedAuto)}
+          <label class="toggle">
+            <span>{t('new.multipleWordsPerTurn')}</span>
+            <input type="checkbox" bind:checked={multipleWords} />
+          </label>
+        {/if}
         <p class="movelimit">{t('new.moveLimit', { n: AUTO_MATCH_HOURS })}</p>
+        <button
+          class="invite"
+          disabled={!selectedAuto || !connection.online}
+          onclick={() => selectedAuto && find(selectedAuto)}
+        >{t('new.start')}</button>
       {:else if friends.length === 0}
         <p class="subtitle">{t('new.noFriends')}</p>
       {:else}
@@ -310,6 +325,12 @@
     font-size: 0.8rem;
     color: var(--text-muted);
   }
+  /* Selected auto-match variant: an accent inset border (the button no longer enqueues on
+     tap; the Start button confirms the choice). */
+  .variant.selected {
+    border-color: var(--accent);
+    box-shadow: inset 0 0 0 2px var(--accent);
+  }
   .movelimit {
     margin: 0;
     text-align: center;