No, it doesn't. If it did, it would be a 700GB+ download and not need OpenAI API keys. Wish folks would stop saying it.
This one doesn’t appear to use a custom prompt, so I’m guessing it doesn’t perform as well as ChatGPT, but it does look like it passes message history.
The key is passed (see https://github.com/ShipBit/slickgpt/blob/main/src/lib/ChatIn...) to a Vercel edge function (see https://github.com/ShipBit/slickgpt/blob/main/src/routes/api...) that does the actual call to the OpenAI API. This function is stateless and doesn't store anything. I also put it in your localStorage using a store (see https://github.com/ShipBit/slickgpt/blob/main/src/misc/store...) so that you don't have to enter it over and over again.
As for the "what is this trying to solve" - read our documentation in the GitHub repo over at https://github.com/ShipBit/slickgpt.