You can actually write an API endpoint that'll retrieve a state token (which inc...

You can actually write an API endpoint that'll retrieve a state token (which includes the cookies). For one example, you can use view our Hacker News login endpoint at https://wrapapi.com/#/view/phsource/hackernews/login/latest

That endpoint will then emit a state token, which includes the session cookies. You can feed that state token into your next request and it'll authenticate you