#Fedilab uses #UnifiedPush for push notifications in every version. The Google Play version comes with a built-in distributor that relies on Google, so notifications work right away. The #FDroid version cannot include that built-in distributor, so you need to install a separate one, like #ntfy or #Sunup. Once it is installed and selected in Fedilab, push works the same way. This is why F-Droid users need an extra app while Google Play users do not. This extra step is not specific to Fedilab.