GitHub Projects doesn't have Issue Types. Your Organisation does.

Let's say you want to add a new kind of Issue Type, like an Epic or a Story or other sort of well-known but not-default-in-projects kind of task. That functionality is not in the Project. Instead, head into your Organisation's settings, then Planning, then Issue Types.

Why you won't find New Issue Types in the Project Settings

An Issue in a Project can be assigned to a Repository, implying that a Repository has to have knowledge of the custom Issue types. By creating custom Issue types at the organisation level, you ensure that every Repository already understands the Issue types that will be associated with it. Custom Issue types showed up before the big announcement last year that GitHub Issues and Projects were becoming more tightly related, so I assume the placing of custom Issue types is related to that timing.

The only reference for what is in a Project's settings is clicking the settings menu item. Note that this page, the index of the Projects docs, doesn't cover Settings. Searching for Project Settings only brings up Repository settings. The joy of working with an evolving featureset 🙂.