Status of the "Android Integration" app

I am using Gotify-UP for push notifications.

Haha, another one who would like to have UnifiedPush integrated.

Or is there another fork / special version of Gadgetbridge for the bangle.js 2?

Gordon is developing a close fork, as he stated above. There wouldn't be fixes like call notifications in there though you wouldn't get in the normal app. The main reason behind the fork is to enable internet access.