As with other OpenAI based applications, I don't feel comfortable sharing my private API key with an application I don't know. Especially when the webpage isn't telling me what this app is about. I suggest adding a small demo video or at least adding some bullets on what this app is trying to solve.
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.