feat(ui): per-kind active-game limit lock on the New Game screen

Carry the caller's per-tier active-game caps and each game's kind on the
wire (Profile.game_limits + GameView.kind, additive FBS + gateway transcode
+ client codec, committed regen). The New Game screen counts the player's
active games per kind from the lobby and locks a capped start: an outline
button with a lock that opens a funnel modal instead of a game -- a sign-in
prompt for a guest, a "finish a current game first" notice for a signed-in
account (native Telegram popup, in-app modal elsewhere). The lock lifts via
the existing profile refetch after a guest->durable upgrade.

Remove the lobby's old at_game_limit New-Game tab disable + notice: the flag
(now the random-kind cap) conflicted with the per-kind lock -- it hid the
screen where the lock lives and wrongly blocked an unfulfilled kind. The New
Game tab is always enabled; the per-kind start lock is the only gate. The
at_game_limit wire field stays (unused by the client) for a later cleanup.

Tests: client lock logic + codec kind/game_limits roundtrip + gateway
transcode encode + native popup builders (unit); a mock e2e for the lock
badge and the modal.

ui/src/components/GameLimitModal.svelte

@@ -0,0 +1,70 @@
+<script lang="ts">
+  import { t } from '../lib/i18n/index.svelte';
+  import { insideTelegram, telegramDialogsAvailable, telegramShowPopup } from '../lib/telegram';
+  import { LOGIN_BUTTON_ID, gameLimitGuestPopup, gameLimitDurablePopup } from '../lib/nativedialogs';
+  import Modal from './Modal.svelte';
+
+  // The New-Game screen raises this when the player taps a start whose kind is at its cap. guest
+  // picks the message: a sign-in funnel (a guest plays more by registering) vs a durable account's
+  // plain "finish a current game first" notice. onclose dismisses; onlogin routes a guest to sign-in.
+  let { open, guest, onclose, onlogin }: { open: boolean; guest: boolean; onclose: () => void; onlogin: () => void } = $props();
+
+  const title = $derived(guest ? t('new.limitGuestTitle') : t('new.limitDurableTitle'));
+  const body = $derived(guest ? t('new.limitGuestBody') : t('new.limitDurableBody'));
+
+  // Native path: inside the Mini App with native dialogs, present Telegram's own popup instead of
+  // the in-app modal (evaluated at fire time — the SDK loads after mount). A guest popup's login
+  // button routes to sign-in; any other dismissal closes. The message here is a plain notice with
+  // no gesture-gated follow-up, so a native popup is safe (unlike share/clipboard flows).
+  let shown = false;
+  $effect(() => {
+    if (open && !shown && insideTelegram() && telegramDialogsAvailable()) {
+      shown = true;
+      const params = guest
+        ? gameLimitGuestPopup(title, body, t('common.cancel'), t('new.limitLogin'))
+        : gameLimitDurablePopup(title, body, t('common.ok'));
+      void telegramShowPopup(params).then((id) => (guest && id === LOGIN_BUTTON_ID ? onlogin() : onclose()));
+    } else if (!open) {
+      shown = false;
+    }
+  });
+</script>
+
+{#if open && !(insideTelegram() && telegramDialogsAvailable())}
+  <Modal {title} onclose={onclose}>
+    <p class="msg">{body}</p>
+    <div class="actions">
+      {#if guest}
+        <button class="cancel" onclick={onclose}>{t('common.cancel')}</button>
+        <button class="primary" onclick={onlogin}>{t('new.limitLogin')}</button>
+      {:else}
+        <button class="primary" onclick={onclose}>{t('common.ok')}</button>
+      {/if}
+    </div>
+  </Modal>
+{/if}
+
+<style>
+  .msg {
+    margin: 0 0 16px;
+    line-height: 1.5;
+  }
+  .actions {
+    display: flex;
+    gap: 8px;
+  }
+  .actions button {
+    flex: 1;
+    padding: 10px 12px;
+    border-radius: var(--radius-sm);
+    border: 1px solid var(--accent);
+  }
+  .cancel {
+    background: transparent;
+    color: var(--accent);
+  }
+  .primary {
+    background: var(--accent);
+    color: var(--accent-text);
+  }
+</style>