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/codec.test.ts

@@ -421,6 +421,7 @@ describe('codec', () => {
     fb.GameView.addLastActivityUnix(b, BigInt(1717000000));
     fb.GameView.addVsAi(b, true);
     fb.GameView.addUnreadChat(b, true);
+    fb.GameView.addKind(b, 2);
     const game = fb.GameView.endGameView(b);
     const games = fb.GameList.createGamesVector(b, [game]);
     fb.GameList.startGameList(b);
@@ -436,6 +437,7 @@ describe('codec', () => {
     expect(gl.games[0].lastActivityUnix).toBe(1717000000);
     expect(gl.games[0].vsAi).toBe(true);
     expect(gl.games[0].unreadChat).toBe(true);
+    expect(gl.games[0].kind).toBe(2);
     expect(gl.atGameLimit).toBe(true);
   });
 
@@ -830,6 +832,26 @@ describe('codec', () => {
     });
   });
 
+  it('decodes the profile active-game limits (guest tier)', () => {
+    const b = new Builder(64);
+    const uid = b.createString('u-1');
+    const limits = fb.GameLimits.createGameLimits(b, 1, 1, 0);
+    fb.Profile.startProfile(b);
+    fb.Profile.addUserId(b, uid);
+    fb.Profile.addGameLimits(b, limits);
+    b.finish(fb.Profile.endProfile(b));
+    expect(decodeProfile(b.asUint8Array()).gameLimits).toEqual({ vsAi: 1, random: 1, friends: 0 });
+  });
+
+  it('leaves the profile game limits undefined when absent', () => {
+    const b = new Builder(64);
+    const uid = b.createString('u-1');
+    fb.Profile.startProfile(b);
+    fb.Profile.addUserId(b, uid);
+    b.finish(fb.Profile.endProfile(b));
+    expect(decodeProfile(b.asUint8Array()).gameLimits).toBeUndefined();
+  });
+
   it('carries the suppressed flag through the ad config', () => {
     const b = new Builder(64);
     const uid = b.createString('u-1');