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/nativedialogs.ts

@@ -8,6 +8,21 @@ import type { TelegramPopupParams } from './telegram';
 /** BOT_BUTTON_ID is the showPopup button id that means "open the bot chat". */
 export const BOT_BUTTON_ID = 'bot';
 
+/** LOGIN_BUTTON_ID is the game-limit popup button that opens the sign-in funnel. */
+export const LOGIN_BUTTON_ID = 'login';
+
+/** gameLimitGuestPopup builds the native popup that nudges a guest to sign in when a New-Game start
+ *  is capped for guests: a cancel button and a login button (the sign-in funnel). */
+export function gameLimitGuestPopup(title: string, message: string, cancelText: string, loginText: string): TelegramPopupParams {
+  return { title, message, buttons: [{ id: 'cancel', text: cancelText }, { id: LOGIN_BUTTON_ID, text: loginText }] };
+}
+
+/** gameLimitDurablePopup builds the native notice shown to a durable account at its per-kind cap:
+ *  an OK button only (finish a current game first). */
+export function gameLimitDurablePopup(title: string, message: string, okText: string): TelegramPopupParams {
+  return { title, message, buttons: [{ id: 'ok', text: okText }] };
+}
+
 /**
  * botInfoPopup builds the native popup for a deep-link info modal: the message with the `{bot}`
  * token replaced by the `@username` as plain text (a native popup has no inline link, unlike the