Store prompts and their responses in a database on Google Cloud

This is a way of caching responses so that we can return already existing data instead of making a new request to the Gemini API every time (which is much more expensive).

No files, tests, or entry points are named in the issue. Start by locating where requests are sent to the Gemini API, then define the Google Cloud database and cache behavior for storing prompts and responses; done means repeated prompts can return stored responses without another Gemini request.

Written by the indexing model from the issue text.