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/lib/lobbycache.test.ts

@@ -27,6 +27,7 @@ function gameView(id: string, status: GameView['status'] = 'active', toMove = 0)
     vsAi: false,
     unreadChat: false,
     unreadMessages: false,
+    kind: 0,
     status,
     players: 2,
     toMove,
@@ -43,7 +44,7 @@ beforeEach(() => clearLobby());
 
 describe('patchLobbyGame', () => {
   it('replaces the matching game by id and leaves the others untouched', () => {
-    setLobby({ games: [gameView('a', 'active', 0), gameView('b', 'active', 0)], invitations: [], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [gameView('a', 'active', 0), gameView('b', 'active', 0)], invitations: [], incoming: [], offline: false });
     // The player's own move flipped game "a" to the opponent's turn.
     patchLobbyGame(gameView('a', 'active', 1));
     const snap = getLobby(false);
@@ -54,14 +55,14 @@ describe('patchLobbyGame', () => {
 
   it('preserves invitations and incoming when patching a game', () => {
     const incoming: AccountRef[] = [{ accountId: 'u9', displayName: 'Nine' }];
-    setLobby({ games: [gameView('a')], invitations: [], incoming, atGameLimit: false, offline: false });
+    setLobby({ games: [gameView('a')], invitations: [], incoming, offline: false });
     patchLobbyGame(gameView('a', 'finished'));
     expect(getLobby(false)?.incoming).toEqual(incoming);
     expect(getLobby(false)?.games[0].status).toBe('finished');
   });
 
   it('adds the game when it is not yet in the cached lobby (a game started elsewhere)', () => {
-    setLobby({ games: [gameView('a')], invitations: [], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [gameView('a')], invitations: [], incoming: [], offline: false });
     patchLobbyGame(gameView('z', 'active'));
     // Order is irrelevant — the lobby re-groups and re-sorts on render — so assert membership.
     expect(getLobby(false)?.games.map((g) => g.id).sort()).toEqual(['a', 'z']);
@@ -74,29 +75,21 @@ describe('patchLobbyGame', () => {
 
   it('does not mutate the previous snapshot array', () => {
     const games = [gameView('a', 'active', 0)];
-    setLobby({ games, invitations: [], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games, invitations: [], incoming: [], offline: false });
     patchLobbyGame(gameView('a', 'active', 1));
     expect(games[0].toMove).toBe(0); // the original array/object is left intact
   });
-
-  it('preserves the at-game-limit flag across a game patch', () => {
-    // A finished-game patch arriving while the lobby is unmounted must not drop the flag —
-    // the lobby renders the "New Game" button from the cached snapshot before the refresh.
-    setLobby({ games: [gameView('a')], invitations: [], incoming: [], atGameLimit: true, offline: false });
-    patchLobbyGame(gameView('a', 'finished'));
-    expect(getLobby(false)?.atGameLimit).toBe(true);
-  });
 });
 
 describe('patchLobbyInvitation', () => {
   it('adds a new pending invitation to the cached lobby', () => {
-    setLobby({ games: [], invitations: [], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [], invitations: [], incoming: [], offline: false });
     patchLobbyInvitation(invitation('i1', 'pending'));
     expect(getLobby(false)?.invitations.map((x) => x.id)).toEqual(['i1']);
   });
 
   it('replaces a pending invitation already in the list (e.g. an updated response)', () => {
-    setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [], offline: false });
     const updated = { ...invitation('i1', 'pending'), turnTimeoutSecs: 999 };
     patchLobbyInvitation(updated);
     expect(getLobby(false)?.invitations.map((x) => x.id)).toEqual(['i1', 'i2']);
@@ -105,14 +98,14 @@ describe('patchLobbyInvitation', () => {
 
   it('removes an invitation that reached a terminal status', () => {
     for (const terminal of ['declined', 'cancelled', 'started', 'expired']) {
-      setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [], atGameLimit: false, offline: false });
+      setLobby({ games: [], invitations: [invitation('i1', 'pending'), invitation('i2', 'pending')], incoming: [], offline: false });
       patchLobbyInvitation(invitation('i1', terminal));
       expect(getLobby(false)?.invitations.map((x) => x.id)).toEqual(['i2']);
     }
   });
 
   it('is a no-op for a terminal invitation that is not in the list', () => {
-    setLobby({ games: [], invitations: [invitation('i2', 'pending')], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [], invitations: [invitation('i2', 'pending')], incoming: [], offline: false });
     patchLobbyInvitation(invitation('i1', 'declined'));
     expect(getLobby(false)?.invitations.map((x) => x.id)).toEqual(['i2']);
   });
@@ -124,7 +117,7 @@ describe('patchLobbyInvitation', () => {
 
   it('preserves games and incoming when patching an invitation', () => {
     const incoming: AccountRef[] = [{ accountId: 'u9', displayName: 'Nine' }];
-    setLobby({ games: [gameView('g1')], invitations: [], incoming, atGameLimit: false, offline: false });
+    setLobby({ games: [gameView('g1')], invitations: [], incoming, offline: false });
     patchLobbyInvitation(invitation('i1', 'pending'));
     expect(getLobby(false)?.games.map((g) => g.id)).toEqual(['g1']);
     expect(getLobby(false)?.incoming).toEqual(incoming);
@@ -133,15 +126,15 @@ describe('patchLobbyInvitation', () => {
 
 describe('getLobby is mode-aware (a mode flip must not render the other mode’s games)', () => {
   it('returns the snapshot only for the mode it was stored under', () => {
-    setLobby({ games: [gameView('online1')], invitations: [], incoming: [], atGameLimit: false, offline: false });
+    setLobby({ games: [gameView('online1')], invitations: [], incoming: [], offline: false });
     expect(getLobby(false)?.games.map((g) => g.id)).toEqual(['online1']);
     // Reading it as the OTHER (offline) mode must not surface the online snapshot.
     expect(getLobby(true)).toBeNull();
   });
 
   it('replaces the snapshot when the mode changes, so the stale mode is dropped', () => {
-    setLobby({ games: [gameView('online1')], invitations: [], incoming: [], atGameLimit: false, offline: false });
-    setLobby({ games: [gameView('local1')], invitations: [], incoming: [], atGameLimit: false, offline: true });
+    setLobby({ games: [gameView('online1')], invitations: [], incoming: [], offline: false });
+    setLobby({ games: [gameView('local1')], invitations: [], incoming: [], offline: true });
     expect(getLobby(false)).toBeNull();
     expect(getLobby(true)?.games.map((g) => g.id)).toEqual(['local1']);
   });