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.

pkg/fbs/scrabble.fbs

@@ -80,6 +80,11 @@ table GameView {
   // message (not just a nudge). With unread_chat it colours the badge — both set is the regular
   // badge, unread_chat alone is the softer nudge-only badge.
   unread_messages:bool;
+  // kind is the game's origin for the active-game limits: 0 unknown (a pre-existing game, never
+  // gated), 1 vs_ai, 2 random, 3 friends. The lobby counts active games per kind against the
+  // caller's per-kind limits (Profile.game_limits) to lock a capped New-Game start (added
+  // trailing — backward-compatible).
+  kind:int;
 }
 
 // MoveRecord is one decoded move (a committed play, or a hint preview).
@@ -267,6 +272,10 @@ table Profile {
   // ads carries the post-move interstitial config (cooldowns + suppressed) for the client-mirrored
   // gate (added trailing — backward-compatible).
   ads:AdsInfo;
+  // game_limits carries the caller's tier active-game caps per kind (-1 = unlimited); the client
+  // counts its active games per kind from the lobby and locks a capped New-Game start (added
+  // trailing — backward-compatible).
+  game_limits:GameLimits;
 }
 
 // AdsInfo is the post-move interstitial config: the client-mirrored cooldowns (seconds) and whether
@@ -278,6 +287,15 @@ table AdsInfo {
   suppressed:bool;
 }
 
+// GameLimits is the caller's tier active-game caps per kind (-1 = unlimited), resolved to the
+// guest or durable tier server-side. It rides Profile.game_limits for the client's per-kind
+// New-Game lock.
+table GameLimits {
+  vs_ai:int;
+  random:int;
+  friends:int;
+}
+
 // BlockStatus reports the caller's current manual block. The UI fetches it after any operation
 // returns the "account_blocked" result code, then replaces every screen with the terminal blocked
 // screen and stops all push/poll. permanent is false for a temporary block; until is an RFC3339