fix(games): carry game kind on live events + fix the New Game lock funnel

Address review of the active-game limit lock:

- Live-event GameViews (opponent_moved, match_found, game_started, ...) did
  not carry game_kind, so a lobby patch from an event zeroed a game's kind
  and the client's per-kind count under-counted — a capped kind read as
  free (a disabled start instead of the lock, and a wrong per-kind result).
  Thread Kind through notify.GameSummary → the event GameView.

- New Game screen refreshes the lobby games on mount so the per-kind count
  reflects the current set, not a stale cached snapshot.

- The guest funnel's login button routes to the profile screen (the account
  controls), not settings.

- Copy: the guest prompt is "sign in to use all the game's features"; the
  durable notice is "finish your active games to start a new one".

Regression tests: the notify opponent-moved payload carries kind; the client
lock locks only the reached kind (vs_ai at cap leaves random open).

ui/e2e/gamelimit.spec.ts

@@ -28,7 +28,7 @@ test('new game: a start locks at its per-kind cap and the funnel modal opens', a
 
   // Tapping the locked start opens the modal instead of a game, and does not navigate away.
   await start.click();
-  const notice = page.getByText(/reached the limit of simultaneous games/i);
+  const notice = page.getByText(/reached the limit/i);
   await expect(notice).toBeVisible();
   await expect(page).toHaveURL(/\/new$/);
   await page.getByRole('button', { name: /^ok$/i }).click();

ui/src/lib/gamelimits.test.ts

@@ -74,4 +74,12 @@ describe('isKindLocked', () => {
   it('a durable account stays well under its higher cap', () => {
     expect(isKindLocked([game(GameKind.random, 'active')], durable, GameKind.random)).toBe(false);
   });
+
+  it('locks only the reached kind: at the vs_ai cap, random with no games stays open', () => {
+    const limits = { vsAi: 3, random: 2, friends: 1 };
+    const games = [game(GameKind.vsAi, 'active'), game(GameKind.vsAi, 'active'), game(GameKind.vsAi, 'active')];
+    expect(isKindLocked(games, limits, GameKind.vsAi)).toBe(true);
+    expect(isKindLocked(games, limits, GameKind.random)).toBe(false);
+    expect(isKindLocked(games, limits, GameKind.friends)).toBe(false);
+  });
 });

ui/src/lib/i18n/en.ts

@@ -380,9 +380,9 @@ export const en = {
   'new.start': 'Start game',
   'new.invited': 'Invitation sent.',
   'new.limitGuestTitle': 'More games?',
-  'new.limitGuestBody': 'Sign in or create an account to play several games at once.',
+  'new.limitGuestBody': 'Sign in or create an account to use all the game features.',
   'new.limitDurableTitle': 'Game limit',
-  'new.limitDurableBody': 'You have reached the limit of simultaneous games — finish a current one first.',
+  'new.limitDurableBody': 'You have reached the limit. Finish your active games to start a new one.',
   'new.limitLogin': 'Sign in',
   'new.noFriends': 'Add friends first to invite them.',
   'new.opponentAI': 'AI',

ui/src/lib/i18n/ru.ts

@@ -380,9 +380,9 @@ export const ru: Record<MessageKey, string> = {
   'new.start': 'Начать игру',
   'new.invited': 'Приглашение отправлено.',
   'new.limitGuestTitle': 'Больше партий?',
-  'new.limitGuestBody': 'Войдите или создайте учётную запись, чтобы играть несколько партий одновременно.',
+  'new.limitGuestBody': 'Войдите или создайте учётную запись, чтобы воспользоваться всеми функциями игры.',
   'new.limitDurableTitle': 'Лимит игр',
-  'new.limitDurableBody': 'Вы достигли лимита одновременных игр, сначала завершите текущие.',
+  'new.limitDurableBody': 'Вы достигли лимита. Доиграйте активные партии, чтобы начать новую.',
   'new.limitLogin': 'Вход',
   'new.noFriends': 'Сначала добавьте друзей, чтобы пригласить их.',
   'new.opponentAI': 'ИИ',

ui/src/screens/NewGame.svelte

@@ -18,7 +18,7 @@
   import { validDisplayName } from '../lib/profileValidation';
   import { verifyPin, type PinLock } from '../lib/pin';
   import { commitName, rosterReady, buildSeats, shuffleSeeded, type RosterRow } from '../lib/roster';
-  import type { AccountRef, Variant } from '../lib/model';
+  import type { AccountRef, GameView, Variant } from '../lib/model';
   import {
     availableVariants,
     VARIANT_FLAG,
@@ -60,7 +60,10 @@
   // funnel modal instead of enqueuing (the server also refuses it); offline never locks (local
   // games are uncapped). The lock lifts when the profile is re-fetched after a guest→durable upgrade.
   const autoKind = $derived(opponent === 'ai' ? GameKind.vsAi : GameKind.random);
-  const autoLocked = $derived(!offlineMode.active && isKindLocked(getLobby(false)?.games ?? [], app.profile?.gameLimits, autoKind));
+  // The player's current games for the per-kind lock: seeded from the lobby snapshot for an instant
+  // render, then refreshed on mount (below) so a game created since the last lobby visit is counted.
+  let lobbyGames = $state<GameView[]>(getLobby(false)?.games ?? []);
+  const autoLocked = $derived(!offlineMode.active && isKindLocked(lobbyGames, app.profile?.gameLimits, autoKind));
   let limitOpen = $state(false);
 
   // --- auto-match ---
@@ -129,6 +132,16 @@
   );
 
   onMount(async () => {
+    // Refresh the lobby games so the per-kind lock counts the current set — the cached snapshot can
+    // lag a game created since the last lobby visit. Online only; the lock never applies offline, and
+    // the server enforces every cap regardless.
+    if (!offlineMode.active && connection.online) {
+      try {
+        lobbyGames = (await gateway.gamesList()).games;
+      } catch {
+        // Keep the cached seed on a transient failure.
+      }
+    }
     // Offline mode offers only the local vs_ai flow (the friends section is hidden), and the network
     // is off, so skip the friend fetch — it would be refused by the transport and toast an error.
     if (guest || offlineMode.active) return;
@@ -349,7 +362,7 @@
           open={limitOpen}
           {guest}
           onclose={() => (limitOpen = false)}
-          onlogin={() => { limitOpen = false; navigate('/settings'); }}
+          onlogin={() => { limitOpen = false; navigate('/profile'); }}
         />
       {:else if offlineMode.active}
         <!-- Offline pass-and-play (hotseat): a device-local 2-4 human game. The host sets a master