If you have a decent GPU or a modern Mac, you can run something like LM Studio (https://lmstudio.ai/) or Ollama (https://ollama.com/), configure the tool such as Cursor to use those models you've downloaded (personally I use Zed.dev), and then everything happens straight on your computer. Responses will be somewhat slower and not as good as state-of-the-art models, but they still can be helpful.

Git host doesn't really make a difference.