You may well be able to do this on-device right now. The latest local models are all capable of tool calls and summarization, which is what this demo needs.
A decent sized Qwen 3 or Gemma 3 might well do the job. Mistral 3.1 Small is great too.
(Personally I'd be happy to pipe my email through an LLM from a respectable vendor that promises not to train on my inputs - Anthropic, OpenAI and Gemini all promise that for paid API usage.)