There is a webpage in german to get an overview (
https://forschungsdaten.info/). I assume that there is not yet a single solution, but a range of possible applications which can be used to connect with each other. GIT actually is the most favorite one for software and there are a lot of common webpage which host them as a service (including NFDI4Ing
https://git.rwth-aachen.de/). There are several tools and services available for research data management. If you need storage for your research data you can use Cosine (
https://about.coscine.de/), Radar (
https://www.radar-service.eu/radar/de/home) or generic services for publication like zenodo (
https://zenodo.org/). If you look for more features to be used during your research process (working with warm data), there are several electronic lab notebook solutions available (Kadi4Mat (diclaimer we develop it), ElabFTW, Chemotion, ScImotion, OpenBIS, ...).