feat: add native Windows broadcaster and live score modules

- streamer/windows: vash-broadcast.exe (setup/login/start/stop/status/doctor)
  with per-instance OBS, tosu and FFmpeg, a supervised worker, OCR room
  selection and OBS scene reconciliation; built and tested on Linux only
- streamer/relay.ts shared with Vash TV; Cloudflare Access proxy for dev/staging
- worker status validation and live score helpers for the site
- STREAMING_HANDOFF.md and streamer/ALPHA_TEST.md record what is unverified

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

streamer/windows/log.ts

@@ -0,0 +1,40 @@
+/** Appends timestamped lines to the instance's log, keeping the last few files. */
+import { appendFileSync, existsSync, mkdirSync, renameSync, rmSync, statSync } from 'node:fs';
+import { dirname } from 'node:path';
+
+const MAX_BYTES = 10 * 1024 * 1024;
+const KEEP = 5;
+
+/** Rotation keeps a multi-hour broadcast's log bounded: worker.log, worker.1.log, … */
+function rotate(path: string) {
+	if (!existsSync(path) || statSync(path).size < MAX_BYTES) return;
+	const numbered = (n: number) => path.replace(/\.log$/, `.${n}.log`);
+	rmSync(numbered(KEEP), { force: true });
+	for (let n = KEEP - 1; n >= 1; n--)
+		if (existsSync(numbered(n))) renameSync(numbered(n), numbered(n + 1));
+	renameSync(path, numbered(1));
+}
+
+export function fileLogger(path: string, alsoConsole = false) {
+	mkdirSync(dirname(path), { recursive: true });
+	let lines = 0;
+	return (...parts: unknown[]) => {
+		const text = parts
+			.map((part) =>
+				part instanceof Error
+					? part.message
+					: typeof part === 'string'
+						? part
+						: JSON.stringify(part)
+			)
+			.join(' ');
+		const line = `${new Date().toISOString()} ${text}\n`;
+		if (alsoConsole) process.stdout.write(line);
+		try {
+			if (++lines % 200 === 0) rotate(path);
+			appendFileSync(path, line);
+		} catch {
+			/* a full or locked disk must not stop the broadcast */
+		}
+	};
+}