Do I need the CUDA toolkit installed to mine Kaspa?

No — the CUDA toolkit is not required to run a Kaspa miner. The CUDA toolkit is a developer package used to compile or modify GPU code at the source level; it is not the same as a GPU driver and does not substitute for one. For everyday mining you only need a proper GPU driver installed on your system. The only reason to install the CUDA toolkit is if you intend to recompile the miner's .cu source files yourself.