At this scale, collaboration would probably slow things down more than it helps. Finding a consensus among so many parties is hard. Building separate solutions first and then unifying them later might be better.
The Stopp Corona app is developed by the Austrian red cross and has already been successfully deployed and used. There's a lot of experience around it.
Why not begin with a fork and add your own requirements? Then slowly try to merge those upstream? Now the landscape is fragmented from the start. It's NIH all over the place.