Add ChatGPT Authentication Functionality

My website was built with the Caffeine framework, and I now need the user-side experience upgraded. Specifically, I want to replace the current login system with one that runs through a ChatGPT API–based plugin.

Here is what I expect:
• Seamless sign-up and sign-in flow that calls the ChatGPT API for authentication and returns a secure token to my site.
• Smooth hand-off so existing Caffeine-generated pages and navigation remain untouched.
• Clear documentation of the code you add—enough for me to maintain or extend the feature later.
• A brief hand-over test session showing that new users can register, existing users can log in, and invalid requests are handled gracefully.

If you have already connected external APIs to Caffeine (or similar PHP/WordPress stacks) that is a bonus, but solid OpenAI/ChatGPT API experience is what matters most.