I don’t know if you caught this in @Coeur-Noir’s reply, or tried it, but in regards to your initial post, the login window wallpaper is set in “Login Window” mentioned in the reply, not settings, budgie-desktop-settings or even tweaks. There are actually 3 different wallpapers you can set - desktop, lock, and login. I actually do have tweaks right now for the sole purpose of this (easily setting a different lock screen and desktop wallpaper.) If I remember correctly, 19.10 at least used to let me select different wallpapers from the Background settings, but not 20.04.
But even still, you still need to use the Login Window app to change the login wallpaper.
I should also mention, I only have one login, so that also may be why it works fine for me.