yt-dlp for page links in every Link mode; app icon and Linux launcher entry

yt-dlp: a managed, checksum-verified, daily-updated yt-dlp in the app and
the dedicated server (--[no-]yt-dlp, --yt-dlp-dir). Pasted links are
probed: direct files stay links, pages are resolved for title, uploader,
duration and thumbnail. Everyone fetches it: mpv's ytdl hook on the
managed copy. I pass it on / the server fetches it: the best single-file
format, re-resolved once when its URL expires. Relay names never split
the /r/ path; viewers of server-fetched pages wait for the relay to go
live. No wire change.

Icon: two stars orbiting a play button (assets/icon/icon.svg, PNGs, the
Windows .ico). GTK app id moe.senkochan.watch_together; release builds
install their .desktop file and icons into ~/.local/share so Wayland
shows the icon; the window icon is set for X11. README shows the icon.

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

apps/desktop/lib/src/state/session_state.dart

@@ -8,6 +8,7 @@ import 'package:sync_relay_core/core.dart';
 
 import '../jellyfin/accounts.dart';
 import '../jellyfin/session_media.dart';
+import '../playback/yt_dlp_app.dart';
 import '../sfx/sfx.dart';
 import '../sfx/synth_sfx.dart';
 import '../session/health.dart';
@@ -165,6 +166,16 @@ class SessionState {
   /// Set when the hosted server died mid-session; Home shows it on the
   /// Host card and clears it.
   final serverCrash = signal<String?>(null);
+
+  /// The app's yt-dlp folder for the hosted server; '' (the server's own
+  /// default) when the app-support folder is not available.
+  static Future<String> _sharedYtDlpDir() async {
+    try {
+      return (await AppYtDlp.instance.ytDlp).dir;
+    } catch (_) {
+      return '';
+    }
+  }
   ServerIsolate? _server;
   String? _setupCrash;
 
@@ -258,6 +269,7 @@ class SessionState {
             mediaPath: params.mediaPath,
             hostKey: hostKey,
             jellyfin: relay,
+            ytDlpDir: await _sharedYtDlpDir(),
           ),
           onLog: (line) => debugPrint('[server] $line'),
           onCrash: (cause) => _onServerCrash(server, cause),