The CMAKE_PREFIX_PATH is set properly. When I try to run nvcc from the installation described above no nvcc is found. If I add nvcc_linux-64 to the environment the last output of the installation is
Cannot determine CUDA_HOME: cuda-gdb not in PATH

Subsequently, which nvcc yields the one in /conda_env/bin/ but running it returns
/conda_env/bin/nvcc: line 2: /bin/nvcc: No such file or directory

This is no surprise as the nvcc in the env itself is nothing but a shell script pointing to the system-wide nvcc. I could set CUDA_HOME manually if I knew where to look for the proper version.