This would be the simplest, if all you're looking to do is play videos. As for the transparent background, Tauri offers transparent backgrounds using this solution. Keep in mind this will only work on non-MacOs environments. For MacOs, you can see the official tauri documentation here

I was able to embed the CLI version of mpv in the Tauri application using RawWindowHandle, tho this method is pretty useless since you don't get control over the running mpv instance.

You can refer to my discord thread:
https://discord.com/channels/616186924390023171/1215223447693692958

You can use libmpv to do the same, and you will have access to pass commands to the mpv player. Only challenge with that route is that the rust bindings for the library are lacking. There's this one: https://github.com/kohsine/libmpv2-rs which supports libmpv v2, but hasn't been updated in months. You can probably do something like:

let mpv = Mpv::with_initializer(|init| {
    init.set_property("vo", "gpu")?;
    init.set_option("wid", window_id as i64)?;
    Ok(())
})
.unwrap();

mpv.command("loadfile", &["http://commondatastorage.googleapis.com/gtv-videos-bucket/sample/BigBuckBunny.mp4", "replace"]).unwrap(); 

I was able to get vlc-rs working with it, which might be the way to go because the bindings are maintained by vlc people and you can get support from their Discord (they were very helpful to me). I had to render the webview in a child window though because vlc kept rendering on top of it if done in the same window.

I was able to embed the CLI version of mpv in the Tauri application using RawWindowHandle, tho this method is pretty useless since you don't get control over the running mpv instance.

You can refer to my discord thread: https://discord.com/channels/616186924390023171/1215223447693692958

You can control mpv playback via JSON IPC
https://github.com/nini22P/mpv-tauri