refactor(web): remove client-side BYO API key feature

The BYO (Bring Your Own) API key configuration for LLM and image
generation will be re-implemented via Cloudflare Workers. Remove
the client-side implementation to prepare for that migration.

TTS (text-to-speech) BYO key support is intentionally preserved.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/api/beat-audio/route.ts

@@ -24,7 +24,7 @@ export async function POST(req: Request) {
   }
 
   try {
-    const config = loadEngineConfig(req.headers);
+    const config = loadEngineConfig();
     const result = await requestBeatAudio(config, body);
     if (!result.audio) return new Response(null, { status: 204 });
     const binary = Buffer.from(result.audio.base64, "base64");