I haven't explored Naninovel's FX much but you could try spawning the effect with a Naninovel script and use it in a PlayScript component attached to the TitleUI, then Play() it through the TitleUI's On Show() event in the inspector, essentially when the TitleUI is visible it will start playing the script automatically.
To despawn it you could do the same but for your title buttons, create another .nani script with a @despawn Rain line, attach a PlayScript component to each button, select the created .nani script, on the button OnClick() event reference the PlayScript component and trigger the Play() method.
You could perhaps do all this in a single custom TitleUI class with these implementations triggering by c#. The logic would still be quite similar I guess.