Document YouTube cookie auth and warn when the file is unusable

Cookies were already wired up but only mentioned in passing, and the
non-obvious parts were undocumented: yt-dlp has no username/password
support for YouTube, it rewrites the cookie file to persist rotated
cookies (so a read-only file expires early), and the export has to
happen in a private window that is logged out before closing.

Startup now reports whether the cookie file is usable, missing, or
read-only, and YTDLP_EXTRACTOR_ARGS is passed through for the cases
where YouTube blocks a server IP outright.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/index.ts

@@ -3,7 +3,7 @@ import { startBot } from "./bot/index.js";
 import { config } from "./config.js";
 import { MusicManager } from "./core/manager.js";
 import { logger } from "./logger.js";
-import { checkYtDlp } from "./sources/index.js";
+import { checkCookies, checkYtDlp } from "./sources/index.js";
 
 async function main(): Promise<void> {
   const ytdlpVersion = await checkYtDlp();
@@ -16,6 +16,18 @@ async function main(): Promise<void> {
     );
   }
 
+  const cookies = await checkCookies();
+  if (cookies === "ok") {
+    logger.info({ path: config.YTDLP_COOKIES }, "using YouTube cookies");
+  } else if (cookies === "read-only") {
+    logger.warn(
+      { path: config.YTDLP_COOKIES },
+      "cookie file is not writable — yt-dlp cannot persist rotated cookies and the session will expire early",
+    );
+  } else if (cookies === "missing") {
+    logger.warn({ path: config.YTDLP_COOKIES }, "cookie file from YTDLP_COOKIES does not exist");
+  }
+
   const manager = new MusicManager();
   const bot = await startBot(manager);
   const app = await startApiServer({ manager, context: bot.context });