Cypress cy.request() does not set Cookies from response

I am trying to is to log in to the testing environment programatically like in the Best Practices.

I've came to the point that I am making valid requests to obtain authorization token and other data like cookies etc - I have this data at the console:

As far as I know cookies at "set-cookie" key from requests' response should be set at the browser. That is not happening - and I think this is the problem why after making these requests I cannot navigate to subpages of the development server of the app.

My investigation led me here: https://github.com/github/fetch/issues/386 -- but I couldn't make use of it. Folks there are saying that there is a problem when you don't define baseUrl. But I did, tried again and still no luck. My cookies are still empty.

This is my code:

as you can see my API URL differs from the server URL - maybe it is useful info.