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/lobbycache.ts

@@ -10,9 +10,6 @@ interface LobbySnapshot {
   games: GameView[];
   invitations: Invitation[];
   incoming: AccountRef[];
-  // atGameLimit rides the snapshot so the lobby renders the "New Game" button in its last
-  // known enabled/disabled state instantly (no flicker), then refreshes it in the background.
-  atGameLimit: boolean;
   // Which mode the snapshot belongs to (offline = device-local games, online = server games). The
   // lobby renders it instantly only when it matches the current mode, so a mode flip never flashes —
   // or lets the player open — the other mode's games before the background refresh replaces them.