GPT4all can do it pretty easily on a desktop with a good GPU. I think it's unlikely that anything can run locally on your phone (LLMs are notably hogs in terms of even pretty capable desktop PC resources; there's just not a cheap way to do them). You could use colab or something via your phone, and there is probably a little howto guide somewhere that shows how to do a Mistral setup on colab. It'll take some technical skill though.
You might just bite the bullet and do $20/mo for the GPT-4 subscription also. It can also do web searches, I think, although in practice it's pretty clunky the times it's tried to do things like that for me. I'm not aware of one that does the "search the web for answers and get back to me" thing really all that perfectly or smoothly I'm sad to say.