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/wire/build.go

@@ -49,6 +49,9 @@ type GameView struct {
 	// UnreadMessages is a per-viewer flag: at least one unread entry is a real message (not just
 	// a nudge), so the badge can be coloured apart from the nudge-only case.
 	UnreadMessages bool
+	// Kind is the game's origin for the active-game limits: 0 unknown (a pre-existing game), 1 vs_ai,
+	// 2 random, 3 friends. The lobby counts active games per kind to lock a capped New-Game start.
+	Kind int
 }
 
 // TileRecord is one tile in a decoded MoveRecord (the concrete letter, "?" for a blank
@@ -169,6 +172,7 @@ func BuildGameView(b *flatbuffers.Builder, g GameView) flatbuffers.UOffsetT {
 	fb.GameViewAddVsAi(b, g.VsAI)
 	fb.GameViewAddUnreadChat(b, g.UnreadChat)
 	fb.GameViewAddUnreadMessages(b, g.UnreadMessages)
+	fb.GameViewAddKind(b, int32(g.Kind))
 	return fb.GameViewEnd(b)
 }