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/gen/fbs/scrabblefb/game-view.ts

@@ -113,8 +113,13 @@ unreadMessages():boolean {
   return offset ? !!this.bb!.readInt8(this.bb_pos + offset) : false;
 }
 
+kind():number {
+  const offset = this.bb!.__offset(this.bb_pos, 34);
+  return offset ? this.bb!.readInt32(this.bb_pos + offset) : 0;
+}
+
 static startGameView(builder:flatbuffers.Builder) {
-  builder.startObject(15);
+  builder.startObject(16);
 }
 
 static addId(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset) {
@@ -189,12 +194,16 @@ static addUnreadMessages(builder:flatbuffers.Builder, unreadMessages:boolean) {
   builder.addFieldInt8(14, +unreadMessages, +false);
 }
 
+static addKind(builder:flatbuffers.Builder, kind:number) {
+  builder.addFieldInt32(15, kind, 0);
+}
+
 static endGameView(builder:flatbuffers.Builder):flatbuffers.Offset {
   const offset = builder.endObject();
   return offset;
 }
 
-static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset, variantOffset:flatbuffers.Offset, dictVersionOffset:flatbuffers.Offset, statusOffset:flatbuffers.Offset, players:number, toMove:number, turnTimeoutSecs:number, multipleWordsPerTurn:boolean, moveCount:number, endReasonOffset:flatbuffers.Offset, seatsOffset:flatbuffers.Offset, lastActivityUnix:bigint, vsAi:boolean, unreadChat:boolean, unreadMessages:boolean):flatbuffers.Offset {
+static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset, variantOffset:flatbuffers.Offset, dictVersionOffset:flatbuffers.Offset, statusOffset:flatbuffers.Offset, players:number, toMove:number, turnTimeoutSecs:number, multipleWordsPerTurn:boolean, moveCount:number, endReasonOffset:flatbuffers.Offset, seatsOffset:flatbuffers.Offset, lastActivityUnix:bigint, vsAi:boolean, unreadChat:boolean, unreadMessages:boolean, kind:number):flatbuffers.Offset {
   GameView.startGameView(builder);
   GameView.addId(builder, idOffset);
   GameView.addVariant(builder, variantOffset);
@@ -211,6 +220,7 @@ static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset,
   GameView.addVsAi(builder, vsAi);
   GameView.addUnreadChat(builder, unreadChat);
   GameView.addUnreadMessages(builder, unreadMessages);
+  GameView.addKind(builder, kind);
   return GameView.endGameView(builder);
 }
 }