How to implement SSO into safari-app-extension without POPOVER toolbar action

Question

I am trying to make SSO auth in my safari-app-extension. And the only way which I found that is creating WKWebView and getting secured cookies from inside. But there are two problems. The first that this is not really SSO, because WKWebView and safari have separated cookie storage. And the second one I don't need POPOVER tollbar item action (all UI composes inside a page). Is there any way to get a seсured cookie from the safari page? Or at least is there any way to invoke/not-to-invoke popover conditionally? I didn't have the same problem in old safari extensions because browser cookies were shared with the background part.