My suggestion would be KDE Neon or Fedora KDE, since both are straightforward and have official Plasma Bigscreen packages
I don't think atomic distros like Bazzite are a good fit for something like this since Plasma Bigscreen does not appear to have an official flatpak. It can be done but there are some drawbacks.
If you go with one of my suggestions, you will want to install multimedia codecs that do not come with the OS by default.