I’m already making custom endpoints to extending that to solve this problem is do-able. After attempting to follow the stack of REST API code, it hasn’t yet surfaced where authentication happens. rest_post_dispatch filter looks like what can be extended to acquire wordpress_logged_in and other cookies.
I asked this question to confirm my initial assumption about the missing cookies and to get a hint on what to fix.
THX!
I see same issue when going to All Pages (using Nested Pages) plugin. I hacked in the 2 lines of changes in the referened Github link and the problem persists.