This is a plugin I found recently and really enjoy. It gives you the opportunity to redirect several webpages to alternatives. For example Youtube to FreeTube or Piped. If I search for youtube in Firefox, FreeTube automatically opens and shows me my feed. I like it, I use it, I can recommend it.
Install it on your Chromecast, that’s what I’ve done. No you can’t cast but you can log in and find your history and such and pull the video up there