Missing Cuda Template VS 2022

I wanted to start with CUDA, followed the instruction guide for installation, but I now have the problem that there is no CUDA template in my VS 2022 Community.
I’ve checked nvcc --version and CUDA is indeed installed correctly, however I’ve read the thread (CUDA 11.6 missing project templates in visual studio 2022) which is talking about the exact same problem, but in my case there is no CUDA 11.6 Wizards\11.6 in my \Microsoft Visual Studio\2022\Community\Common7\IDE\Extensions\NVIDIA directory (only Nsight Visual Studio Edition - it tells me tho, that the VS integration was successfully installed for both VS 2019 and 2022 when the CUDA installation is finished) . Is there a way to integrate it manually?

I had the same issue and was just able to get a solution.