Chat + word-check as their own screens; in-game unread badge (review item 7)

- Chat and word-check are now routed screens (/game/:id/chat, /game/:id/check) with a
  header back to the game and no tab-bar, replacing their modals. The soft keyboard just
  resizes the visible viewport (tracked into --vvh, which the Screen height uses since iOS
  does not shrink dvh for the keyboard) with the input pinned to the bottom: no modal
  relayout, no page jump. Supersedes the earlier bottom-sheet Modal attempt.
- A new chat message raises an unread badge on the in-game hamburger + the Chat menu row
  (per game, cleared on opening the chat), mirroring the lobby badge.
- TG native back + the header back chevron return chat/check to their game.
- Exposes --tg-safe-top (device notch) for the finalised TG-fullscreen header.

Tests: e2e for chat/check opening as their own screens + back. Docs: PLAN, FUNCTIONAL(+ru).

ui/src/game/Game.svelte

@@ -7,17 +7,16 @@
   import Modal from '../components/Modal.svelte';
   import Board from './Board.svelte';
   import Rack from './Rack.svelte';
-  import Chat from './Chat.svelte';
   import { gateway } from '../lib/gateway';
+  import { navigate } from '../lib/router.svelte';
   import { app, handleError, showToast } from '../lib/app.svelte';
   import { GatewayError } from '../lib/client';
   import { t } from '../lib/i18n/index.svelte';
-  import type { ChatMessage, Direction, EvalResult, MoveRecord, StateView, Tile } from '../lib/model';
+  import type { Direction, EvalResult, MoveRecord, StateView, Tile } from '../lib/model';
   import { replay } from '../lib/board';
   import { centre, premiumGrid } from '../lib/premiums';
   import { variantNameKey } from '../lib/variants';
   import { alphabetLetters, hasAlphabet } from '../lib/alphabet';
-  import { canCheckWord, sanitizeCheckWord } from '../lib/checkword';
   import { shareOrDownloadGcg } from '../lib/share';
   import { getCachedGame, setCachedGame } from '../lib/gamecache';
   import { telegramClosingConfirmation, telegramHaptic } from '../lib/telegram';
@@ -50,21 +49,13 @@
   // tiles fly to their new positions (Rack's hop animation) instead of relabelling in place.
   let rackIds = $state<number[]>([]);
   let shuffling = $state(false);
-  let panel = $state<'none' | 'chat'>('none');
   let historyOpen = $state(false);
   let blankPrompt = $state<{ rackIndex: number; row: number; col: number } | null>(null);
   let exchangeOpen = $state(false);
   let exchangeSel = $state<number[]>([]);
-  let checkOpen = $state(false);
-  let checkWord = $state('');
-  let checkResult = $state<{ word: string; legal: boolean } | null>(null);
   let resignOpen = $state(false);
-  let messages = $state<ChatMessage[]>([]);
   let drag = $state<{ letter: string; blank: boolean; x: number; y: number; touch: boolean } | null>(null);
 
-  const checkedWords = new Map<string, boolean>();
-  let cooling = $state(false);
-
   const variant = $derived(view?.game.variant ?? 'english');
   const board = $derived(replay(moves));
   const premium = $derived(premiumGrid(variant));
@@ -96,29 +87,6 @@
   const isMyTurn = $derived(!!view && view.game.status === 'active' && view.game.toMove === view.seat);
   const gameOver = $derived(!!view && view.game.status !== 'active');
   const bagEmpty = $derived((view?.bagLen ?? 0) === 0);
-  // Nudge cooldown (one per hour per game, mirrored from the backend): the control is
-  // disabled for an hour after the player's own last nudge. nudgeTick re-evaluates it on a
-  // timer while the chat is open, so it re-enables without waiting for a new message.
-  const nudgeCooldownSecs = 3600;
-  let nudgeTick = $state(0);
-  // Unix seconds of the player's own last move, which resets the nudge cooldown (mirrors the
-  // backend, Stage 17). A chat reset is read from `messages`; a move is tracked client-side
-  // (the backend stays authoritative across a reload).
-  let lastActedAt = $state(0);
-  const nudgeOnCooldown = $derived.by(() => {
-    void nudgeTick;
-    const mine = app.session?.userId ?? '';
-    let lastNudge = 0;
-    let lastChat = 0;
-    for (const m of messages) {
-      if (m.senderId !== mine) continue;
-      if (m.kind === 'nudge') lastNudge = Math.max(lastNudge, m.createdAtUnix);
-      else lastChat = Math.max(lastChat, m.createdAtUnix);
-    }
-    if (lastNudge === 0 || Date.now() / 1000 - lastNudge >= nudgeCooldownSecs) return false;
-    // Engagement since the nudge clears the cooldown: a chat or a move.
-    return lastChat <= lastNudge && lastActedAt <= lastNudge;
-  });
 
   async function load() {
     try {
@@ -169,13 +137,6 @@
     const rack = order.map((i) => st.rack[i]);
     placement = tiles.length ? placementFromHint(tiles, rack) : newPlacement(rack);
   }
-  async function loadChat() {
-    try {
-      messages = await gateway.chatList(id);
-    } catch (e) {
-      handleError(e);
-    }
-  }
   onMount(() => {
     // Guard against an accidental swipe-close losing the open game (Telegram).
     telegramClosingConfirmation(true);
@@ -200,20 +161,11 @@
       // player's other devices): this device already reloaded after the submit.
       if (e.seat !== view?.seat) void load();
     } else if (e.kind === 'your_turn' && e.gameId === id) void load();
-    else if (e.kind === 'chat_message' && e.message.gameId === id && panel === 'chat') void loadChat();
-    else if (e.kind === 'nudge' && e.gameId === id && panel === 'chat') void loadChat();
     // A request the player sent was answered (accepted -> now friends; declined -> stays
     // "request sent"): re-derive the in-game friend state.
     else if (e.kind === 'notify' && (e.sub === 'friend_added' || e.sub === 'friend_declined')) void loadFriends();
   });
 
-  // Tick the nudge cooldown while the chat is open so the control re-enables on time.
-  $effect(() => {
-    if (panel !== 'chat') return;
-    const h = setInterval(() => (nudgeTick += 1), 20000);
-    return () => clearInterval(h);
-  });
-
   function isCoarse(): boolean {
     return typeof matchMedia !== 'undefined' && matchMedia('(pointer: coarse)').matches;
   }
@@ -499,7 +451,6 @@
     busy = true;
     try {
       await gateway.submitPlay(id, sub.dir, sub.tiles, variant);
-      lastActedAt = Date.now() / 1000; // a move resets the nudge cooldown
       telegramHaptic('success');
       zoomed = false;
       await load();
@@ -521,7 +472,6 @@
     busy = true;
     try {
       await gateway.pass(id);
-      lastActedAt = Date.now() / 1000; // a move resets the nudge cooldown
       await load();
     } catch (e) {
       handleError(e);
@@ -603,7 +553,6 @@
     busy = true;
     try {
       await gateway.exchange(id, tiles, variant);
-      lastActedAt = Date.now() / 1000; // a move resets the nudge cooldown
       await load();
     } catch (e) {
       handleError(e);
@@ -612,64 +561,6 @@
     }
   }
 
-  function openCheck() {
-    checkWord = '';
-    checkResult = null;
-    checkOpen = true;
-  }
-  function onCheckInput(e: Event) {
-    checkWord = sanitizeCheckWord((e.target as HTMLInputElement).value, alphabetLetters(variant));
-  }
-  // Check is disabled while cooling down, for an already-checked word, or an out-of-range
-  // length. The input filter already restricts to the variant's alphabet.
-  function canCheck(): boolean {
-    return canCheckWord(checkWord, checkedWords.has(checkWord.trim().toUpperCase()), cooling);
-  }
-  async function runCheck() {
-    if (!canCheck()) return;
-    const w = checkWord.trim().toUpperCase();
-    cooling = true;
-    setTimeout(() => (cooling = false), 5000);
-    try {
-      const r = await gateway.checkWord(id, w, variant);
-      // Key the cache and the displayed result on the upper-case word the player typed; the
-      // server echoes the decoded concrete word in the solver's lower case.
-      checkedWords.set(w, r.legal);
-      checkResult = { word: w, legal: r.legal };
-    } catch (e) {
-      handleError(e);
-    }
-  }
-  async function complain() {
-    if (!checkResult) return;
-    try {
-      await gateway.complaint(id, checkResult.word, '');
-      showToast(t('game.complaintSent'));
-      checkOpen = false;
-    } catch (e) {
-      handleError(e);
-    }
-  }
-
-  function openChat() {
-    panel = 'chat';
-    void loadChat();
-  }
-  async function sendChat(text: string) {
-    try {
-      messages = [...messages, await gateway.chatPost(id, text)];
-    } catch (e) {
-      handleError(e);
-    }
-  }
-  async function nudge() {
-    try {
-      messages = [...messages, await gateway.nudge(id)];
-    } catch (e) {
-      handleError(e);
-    }
-  }
-
   function resultText(): string {
     if (!view) return '';
     const me = view.game.seats[view.seat];
@@ -724,8 +615,8 @@
   // an "add to friends" item flips to a disabled "request sent" once tapped.
   const menuItems = $derived([
     { label: t('game.history'), onclick: () => (historyOpen = true) },
-    { label: t('game.chat'), onclick: openChat },
-    ...(gameOver ? [] : [{ label: t('game.checkWord'), onclick: openCheck }]),
+    { label: t('game.chat'), onclick: () => navigate(`/game/${id}/chat`), badge: app.chatUnread[id] ?? 0 },
+    ...(gameOver ? [] : [{ label: t('game.checkWord'), onclick: () => navigate(`/game/${id}/check`) }]),
     ...(view?.game.status === 'finished' ? [{ label: t('game.exportGcg'), onclick: exportGcg }] : []),
     ...(!app.profile?.isGuest
       ? opponents.map((s) =>
@@ -742,7 +633,7 @@
 
 <Screen title={t(variantNameKey(variant))} back="/" growNav column scroll={false}>
   {#snippet menu()}
-    <Menu items={menuItems} />
+    <Menu items={menuItems} badge={app.chatUnread[id] ?? 0} />
   {/snippet}
 
   {#if view}
@@ -898,28 +789,6 @@
   </Modal>
 {/if}
 
-{#if checkOpen}
-  <Modal title={t('game.checkWord')} overlayKeyboard onclose={() => (checkOpen = false)}>
-    <div class="check">
-      <input
-        value={checkWord}
-        oninput={onCheckInput}
-        onkeydown={(e) => e.key === 'Enter' && runCheck()}
-        placeholder={t('game.checkWordPrompt')}
-      />
-      <button onclick={runCheck} disabled={!canCheck()}>{t('game.check')}</button>
-    </div>
-    {#if checkResult}
-      <p class:ok={checkResult.legal} class:bad={!checkResult.legal}>
-        {checkResult.legal
-          ? t('game.wordLegal', { word: checkResult.word })
-          : t('game.wordIllegal', { word: checkResult.word })}
-      </p>
-      <button class="complain" onclick={complain}>{t('game.complain')}</button>
-    {/if}
-  </Modal>
-{/if}
-
 {#if resignOpen}
   <Modal title={t('game.confirmResign')} onclose={() => (resignOpen = false)}>
     <div class="confirm-row">
@@ -929,12 +798,6 @@
   </Modal>
 {/if}
 
-{#if panel === 'chat'}
-  <Modal title={t('game.chat')} bottomSheet onclose={() => (panel = 'none')}>
-    <Chat {messages} myId={app.session?.userId ?? ''} {busy} myTurn={isMyTurn} {nudgeOnCooldown} onsend={sendChat} onnudge={nudge} />
-  </Modal>
-{/if}
-
 <style>
   .scoreboard {
     display: flex;
@@ -1193,38 +1056,6 @@
   .confirm:disabled {
     opacity: 0.5;
   }
-  .check {
-    display: flex;
-    gap: 6px;
-  }
-  .check input {
-    flex: 1;
-    padding: 10px;
-    border: 1px solid var(--border);
-    border-radius: var(--radius-sm);
-    background: var(--bg);
-    color: var(--text);
-    text-transform: uppercase;
-  }
-  .check button {
-    padding: 10px 12px;
-    border: 1px solid var(--border);
-    background: var(--surface);
-    color: var(--text);
-    border-radius: var(--radius-sm);
-  }
-  .ok {
-    color: var(--ok);
-  }
-  .bad {
-    color: var(--danger);
-  }
-  .complain {
-    background: none;
-    border: none;
-    color: var(--accent);
-    padding: 4px 0;
-  }
   .confirm-row {
     display: flex;
     gap: 8px;