You might be able to convince Firefox to be transparent with a GTK theme as Firefox uses GTK under the hood for the window. If you’re lucky it won’t bother clearing it with black just in case and it’ll actually be transparent.
The shader option is pretty neat and easy though.
Post the Hyprland config too?
Does it make the entire screen green by chance, not just the windows? If the shader applies to the whole screen, then setting alpha on it doesn’t really makes sense and is probably discarded since your monitor can’t display transparency. You need to make sure it applies on a per-window basis for them to be composited as transparent and show your wallpaper behind it.