Chromecast support is on hold because F-droid doesn’t allow gms proprietary libraries: https://github.com/jarnedemeulemeester/findroid/pull/139
The creator deems theme music to be “annoying” so they won’t add it: https://github.com/jarnedemeulemeester/findroid/issues/105
So no dice, it seems.
As if Google doesn’t already know.