thakurgit/engagifii-sso ? reverse-engineered prompt

Build me a WordPress plugin that lets people log in with Engagifii single sign on.

I want it to work as a normal login option inside WordPress, with a simple admin screen where I can enter the SSO details and turn it on or off. After a user signs in through Engagifii, they should be sent back into WordPress and either get logged in with an existing account or have a new account created if needed.

Please include the front end part for the login flow, the admin settings page, and any helper code needed to keep the plugin organized. It should be clean, easy to activate, and not break the normal WordPress login page.

If anything about the Engagifii login flow or API details is unclear, look up the current docs online and wire it up the best way you can.