feat(ui): refine Telegram invite & close UX

- Shared invite links open the Mini App fullscreen (mode=fullscreen), so a
  shared link matches the bot's own fullscreen launch.
- A used or expired invite deep-link now lands the visitor in the lobby with a
  gentle notice pointing at the right bot (@<username>, by service language),
  instead of a red "code invalid/expired" error on the Friends screen.
- The in-game close confirmation is armed only on Telegram mobile clients; on
  desktop (tdesktop/macOS/web) it is skipped, where the "changes may not be
  saved" dialog is just noise (drafts auto-save).

ui/src/lib/deeplink.ts

@@ -52,6 +52,23 @@ function telegramBase(lang: string): string | null {
   return byLang || envVar('VITE_TELEGRAM_LINK') || null;
 }
 
+/**
+ * botUsername extracts the bot's @username (without the @) from the configured Mini App
+ * link for a bot language: the first path segment of https://t.me/<bot>/<app>. Returns
+ * null when no base is configured or the link carries no path, so callers can fall back
+ * when they cannot point at a specific bot.
+ */
+export function botUsername(lang = ''): string | null {
+  const base = telegramBase(lang);
+  if (!base) return null;
+  try {
+    const seg = new URL(base).pathname.split('/').filter(Boolean)[0];
+    return seg || null;
+  } catch {
+    return null;
+  }
+}
+
 /**
  * shareLink wraps a deep-link start parameter in a t.me Mini App link for the given
  * bot language (the session's service language). Returns null when no base is
@@ -61,5 +78,7 @@ export function shareLink(param: string, lang = ''): string | null {
   const base = telegramBase(lang);
   if (!base) return null;
   const sep = base.includes('?') ? '&' : '?';
-  return `${base}${sep}startapp=${encodeURIComponent(param)}`;
+  // mode=fullscreen opens the Mini App fullscreen, matching how the bot's own entry
+  // opens it, so a shared link and the bot give the same experience.
+  return `${base}${sep}startapp=${encodeURIComponent(param)}&mode=fullscreen`;
 }