feat: sign in to YouTube with browser cookies

Answers the bot challenge from inside the app. Settings gains a browser
picker listing only the browsers actually installed; choosing one passes
--cookies-from-browser to every yt-dlp call, so YouTube sees an
authenticated session. Verified against a live block: refused without
cookies, resolved with them.

Arc is Chromium underneath but is not one of yt-dlp's known names, so it
is addressed by its profile directory instead.

yt-dlp's errors are translated into something actionable. The stock bot
message points at command-line flags a user cannot type; it now names
the setting that fixes it, and Safari's protected cookie store gets its
own message about Full Disk Access rather than a bare 'Operation not
permitted'.

A Check connection button reports whether YouTube is reachable, testing
against the newest video in the feed — the hardcoded id it used at first
had been taken down, so it reported a dead video rather than the
connection.

src/App.tsx

@@ -1,7 +1,7 @@
 import { useCallback, useEffect, useMemo, useRef, useState } from "react";
 import {
   cancelDownload, deleteAllDownloads, deleteDownload, downloadVideo,
-  fetchDurations, onRefreshProgress, refreshFeeds,
+  fetchDurations, onRefreshProgress, refreshFeeds, setCookieSource,
 } from "./api";
 import Player from "./components/Player";
 import Settings from "./components/Settings";
@@ -55,6 +55,13 @@ export default function App() {
   const [showSettings, setShowSettings] = useState(false);
   // Index into the current feed, so the player can step through it.
   const [playingIndex, setPlayingIndex] = useState<number | null>(null);
+  const [browser, setBrowser] = useState(() => {
+    try {
+      return localStorage.getItem("flighttube.browser") ?? "";
+    } catch {
+      return "";
+    }
+  });
   const [subLang, setSubLang] = useState(() => {
     try {
       const stored = localStorage.getItem("flighttube.subLang");
@@ -84,6 +91,14 @@ export default function App() {
   const [toast, setToast] = useState<string | null>(null);
   const [failure, setFailure] = useState<string | null>(null);
 
+  // The backend holds no state across launches, so the stored choice has to be
+  // handed back to it before the first yt-dlp call.
+  useEffect(() => {
+    setCookieSource(browser).catch(() => {
+      /* falls back to no cookies */
+    });
+  }, [browser]);
+
   const { mode, setMode } = useAppearance();
   const windowFullscreen = useWindowFullscreen();
   const { online, reachable, forcedOffline, setForcedOffline, probe } = useConnectivity();
@@ -104,13 +119,14 @@ export default function App() {
       localStorage.setItem("flighttube.quality", quality);
       localStorage.setItem("flighttube.streamQuality", streamQuality);
       localStorage.setItem("flighttube.subLang", subLang);
+      localStorage.setItem("flighttube.browser", browser);
       localStorage.setItem("flighttube.downloadedOnly", downloadedOnly ? "1" : "0");
       localStorage.setItem("flighttube.hideShorts", hideShorts ? "1" : "0");
       localStorage.setItem("flighttube.sidebarHidden", sidebarHidden ? "1" : "0");
     } catch {
       /* storage blocked */
     }
-  }, [view, quality, streamQuality, subLang, downloadedOnly, hideShorts, sidebarHidden]);
+  }, [view, quality, streamQuality, subLang, browser, downloadedOnly, hideShorts, sidebarHidden]);
 
   // Offline, the only videos that can be played are the ones already on disk,
   // so the feed collapses to those regardless of the toggle.
@@ -459,6 +475,8 @@ export default function App() {
           onStreamQuality={setStreamQuality}
           subLang={subLang}
           onSubLang={setSubLang}
+          browser={browser}
+          onBrowser={setBrowser}
           onError={setFailure}
           onImported={(n) => {
             reload();