API key is optional -- that's only if you want to use the hosted vector database. When running locally, no Vanna API key is necessary. Instead, you can put in an OpenAI API key as shown here: https://vanna.ai/docs/local.html

If you want to use a locally-hosted LLM, that's also possible by implementing the necessary abstract methods: https://vanna.ai/docs/vanna.html#open-source-and-extending