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.ts

@@ -15,6 +15,7 @@ import type {
   RobotFriendRequestEntry,
   Banner,
   AdsConfig,
+  GameLimits,
   BannerCampaign,
   BestMove,
   BestMoveTile,
@@ -314,6 +315,7 @@ function decodeGameView(g: fb.GameView): GameView {
     vsAi: g.vsAi(),
     unreadChat: g.unreadChat(),
     unreadMessages: g.unreadMessages(),
+    kind: g.kind(),
     seats,
   };
 }
@@ -467,9 +469,18 @@ export function decodeProfile(buf: Uint8Array): Profile {
     telegramLinked: p.telegramLinked(),
     vkLinked: p.vkLinked(),
     dictVersions: decodeDictVersions(p),
+    gameLimits: decodeGameLimits(p),
   };
 }
 
+// decodeGameLimits projects the caller's tier active-game caps (per kind, -1 = unlimited), or
+// undefined when absent (an old backend); the New-Game screen then applies no lock.
+function decodeGameLimits(p: fb.Profile): GameLimits | undefined {
+  const g = p.gameLimits();
+  if (!g) return undefined;
+  return { vsAi: g.vsAi(), random: g.random(), friends: g.friends() };
+}
+
 // decodeDictVersions reads the profile's per-variant current dictionary versions into a
 // variant-keyed map, so the offline preloader can look up the version for each enabled
 // variant. An entry with an unknown variant or empty version is skipped.
@@ -1137,6 +1148,7 @@ function emptyGame(): GameView {
     vsAi: false,
     unreadChat: false,
     unreadMessages: false,
+    kind: 0,
     seats: [],
   };
 }