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.

gateway/internal/transcode/encode.go

@@ -194,6 +194,15 @@ func encodeProfile(p backendclient.ProfileResp) []byte {
 		fb.AdsInfoAddSuppressed(b, p.Ads.Suppressed)
 		ads = fb.AdsInfoEnd(b)
 	}
+	// The active-game limits table (scalars only), built before Profile is opened.
+	var gameLimits flatbuffers.UOffsetT
+	if p.GameLimits != nil {
+		fb.GameLimitsStart(b)
+		fb.GameLimitsAddVsAi(b, int32(p.GameLimits.VsAI))
+		fb.GameLimitsAddRandom(b, int32(p.GameLimits.Random))
+		fb.GameLimitsAddFriends(b, int32(p.GameLimits.Friends))
+		gameLimits = fb.GameLimitsEnd(b)
+	}
 	fb.ProfileStart(b)
 	fb.ProfileAddUserId(b, uid)
 	fb.ProfileAddDisplayName(b, name)
@@ -219,6 +228,9 @@ func encodeProfile(p backendclient.ProfileResp) []byte {
 	if p.Ads != nil {
 		fb.ProfileAddAds(b, ads)
 	}
+	if p.GameLimits != nil {
+		fb.ProfileAddGameLimits(b, gameLimits)
+	}
 	b.Finish(fb.ProfileEnd(b))
 	return b.FinishedBytes()
 }
@@ -624,6 +636,7 @@ func toWireGame(g backendclient.GameResp) wire.GameView {
 		LastActivityUnix:     g.LastActivityUnix,
 		UnreadChat:           g.UnreadChat,
 		UnreadMessages:       g.UnreadMessages,
+		Kind:                 g.Kind,
 	}
 }