setBackgroundDrawable() deprecated

It’s an interesting topic. The way you are doing it is correct, apparently. It is actually just a naming decision change. As this answer points out, setBackground() just calls setBackgroundDrawable():

public void setBackground(Drawable background) {
    //noinspection deprecation
    setBackgroundDrawable(background);
}

@Deprecated
public void setBackgroundDrawable(Drawable background) { ... }

You can see this thread for more information about all of this.