We have both schedule_look_emails and schedule_external_look_emails granted to the user. Here is the full list:
So as embed user I do see Schedule and I can do it. Also, I can save to a space.
The issue is I do not see Share item. Our use case is a user creates a Look, then generates short URL using Share and gives it to another user as a quick share mechanism.
We can tell the users to always go through save as a look and just provide a name to another user to look at it, but Share feature is much nicer and I am not sure why embed user does not see it.