if a.com is open in one tab, and b.com in another, then synchronising refresh API calls is not possible using cookies nor localstorage...
If a user logs in via a.com, the API domain has cookies set against them. Now if the user logs into b.com, the cookies in the APIs are over written. What happens to a.com's session?
If user logs out of a.com, then b.com might still think that the user is logged in..
Some example issues: