fix: remove redundant ts-broadcasting type declaration

ts-broadcasting ships its own .d.ts files. The manual declaration was
only needed when the package was a broken bun link. Fixed broadcastPrivate
to use Broadcast.send with private- prefix (no .private() method exists).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: glennmichael123

packages/stx/src/broadcasting.ts

@@ -267,7 +267,7 @@ export function broadcastPrivate<T = unknown>(
   data: T,
 ): void {
   if (!isReady()) return
-  Broadcast.private(channelName, event, data)
+  Broadcast.send(`private-${channelName}`, event, data)
 }
 
 /**