Miracast (e.g. vis Miraclecast on linux) is a wireless standard for streaming video and audio from one device to another however this is not quite what youre talking about. Miracast basically runs the video on your phone and uses a remote device as a display via wifi. Chromecast actually mostly sends a link to a google device and then launches it on the device to play; there isnt a direct replacement to that. You could run Chrome or Chromium and cast to the browser but im not sure it'd work like a chromecaat device running the video locally.
I have a living room linux PC and I generally use Firefox on my phone and the PC to send links/tabs via firefox sync.
In addition KDE Connect (app on phone and also running on your linux PC) allows you to interact with your PC directly via your phone. You can send files back and forth, but also control media, share the clipboard, and send URLs from your phone to your PC to open in your default browser. This should work for Youtube and Netflix etc.
I personally usually send a tab to my firefox browser via firefox sync, but you could also share link instead via android share to the KDE connect app which will send it to your device and it should open in you're default browser.
Also fyi KDE Connect doesnt need KDE to work - it works with any desktop environment.
As you can see the UI was clunky and I guess it's part of the reasons why it died. Too bad, I like the concept of having a jukebox at a party where people can just contribute to without installing anything, let alone sign up for an account.