At the moment Shopify does not offer a Navigation API, and unfortunately there isn't a way to generate menu items automatically based on certain conditions. You will need to manually create menu items using the navigation settings in the Shopify admin (found under Online Store > Navigation).
Hopefully this helps!
From my understanding the only way to create menu items is via the navigation settings in the Shopify admin. It looks like the GraphQL version of the Admin API includes a NavigationItem object, but I am not personally familiar with it: https://shopify.dev/docs/admin-api/graphql/reference/store-properties/navigationitem