Laravel: Not setting cookies on client with vuejs?

Question

Laravel

I am writing an application in vue along with a backender, backend in laravel.
We are stuck on cross-domain authentication.
The logic is this:
When a user is authorized, the backend sends cookies so that they are saved in the browser and when visiting subdomains using this cookie, I could implement authentication.
But cookies are not set. The backender thinks this is because the client is interacting with the domain itself and not the api from the backend, and that I have to set cookies myself in each subdomain.
The application has work with the unsplash.com api and when making requests to the unsplash.com api, cookies from unsplash.com are normally set in the browser. I specifically downloaded the unsplash-js plugin, through which I make requests and there is no cookie setting via js.
Tell me, is it correct that I should set cookies in the front on each subdomain or should it be done from the backend?