refactor: flatten monorepo to single web package (#12)

Flatten the pnpm monorepo (apps/web + packages/*) into a single web package at the repo root.

- Move app/lib/components/scripts/public to root; drop apps/web and packages/* wrappers
- Rewrite tsconfig paths (@infiplot/*) to ./lib/*; turbopack.root = __dirname
- Update Vercel (no root-directory) and Cloudflare (pnpm build:cf at root) deploy paths
- Regenerate pnpm-lock.yaml to drop stale workspace importers
- Bump engines.node to >=22 to match wrangler

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

app/api/beat-audio/route.ts

@@ -0,0 +1,36 @@
+import { requestBeatAudio } from "@infiplot/engine";
+import type { BeatAudioRequest } from "@infiplot/types";
+import { NextResponse } from "next/server";
+import { loadEngineConfig } from "@/lib/config";
+
+export const runtime = "nodejs";
+// The synth itself has a 15s per-call ceiling in the engine. 30s here just
+// covers JSON parsing + outbound network buffer.
+export const maxDuration = 30;
+
+export async function POST(req: Request) {
+  let body: BeatAudioRequest;
+  try {
+    body = (await req.json()) as BeatAudioRequest;
+  } catch {
+    return NextResponse.json({ error: "Invalid JSON" }, { status: 400 });
+  }
+
+  if (!body.beat?.id || !body.beat?.line || !body.voice?.referenceAudioBase64) {
+    return NextResponse.json(
+      { error: "beat.id, beat.line and voice.referenceAudioBase64 are required" },
+      { status: 400 },
+    );
+  }
+
+  try {
+    const config = loadEngineConfig();
+    const result = await requestBeatAudio(config, body);
+    return NextResponse.json(result);
+  } catch (err) {
+    // Engine already swallows synth errors and returns audio:null. Anything
+    // that reaches here is config-level — surface so the client can log it.
+    const message = err instanceof Error ? err.message : "Unknown error";
+    return NextResponse.json({ error: message }, { status: 500 });
+  }
+}